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Substitution Method

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Question 1 of 18

Solve the following simultaneous equations by substitution.

$x-y=8$

$2x+y=1$

$x=$ (3)

$y=$ (-5)

Question 2 of 18

Solve the following simultaneous equations by substitution.

$2x-y=6$

$x+3y=10$

$x=$ (4)

$y=$ (2)

Question 3 of 18

Solve the following simultaneous equations by substitution.

$2a+b=5$

$5a-3b=7$

$a=$ (2)

$b=$ (1)

Question 4 of 18

Solve the following simultaneous equations by substitution.

$2x+y=1$

$x-y=2$

$x=$ (1)

$y=$ (-1)

Question 5 of 18

Solve the following simultaneous equations by substitution.

$x-y=1$

$2x+y=11$

$x=$ (4)

$y=$ (3)

Question 6 of 18

Solve the following simultaneous equations by substitution.

$2x+y=7$

$4x-2y=10$

$x=$ (3)

$y=$ (1)

Question 7 of 18

Solve the following simultaneous equations by substitution.

$a-3b=2$

$2a-b=14$

$a=$ (8)

$b=$ (2)

Question 8 of 18

Solve the following simultaneous equations by substitution.

$3x-2y=20$

$x+2y=-4$

$x=$ (4)

$y=$ (-4)

Question 9 of 18

Solve the following simultaneous equations by substitution.

$2x+5y=7$

$x-y=7$

$x=$ (6)

$y=$ (-1)

Question 10 of 18

Solve the following simultaneous equations by substitution.

$a-b=5$

$2a+b=4$

$a=$ (3)

$b=$ (-2)

Question 11 of 18

Solve the following simultaneous equations by substitution.

$b=2a+2$

$2a+5b=10$

$a=$ (0)

$b=$ (2)

Question 12 of 18

Solve the following simultaneous equations by substitution.

$2m+5n=5$

$m-5n=10$

$m=$ (5)

$n=$ (-1)

Question 13 of 18

Solve the following simultaneous equations by substitution.

$8a+5b=6$

$4a+2b=4$

$a=$ (2)

$b=$ (-2)

Question 14 of 18

Solve the following simultaneous equations by substitution.

$2x+5y=17$

$3x+3y=12$

$x=$ (1)

$y=$ (3)

Question 15 of 18

Solve the following simultaneous equations by substitution.

$3x+7y=4$

$2x+3y=1$

$x=$ (-1)

$y=$ (1)

Incorrect

Help Video

Substitution Method

$1)$ make one variable the subject
$2)$ substitute into second equation
$3)$ solve the second equation
$4)$ substitute back

First, label the two equations

$1$ and

$2$ respectively.

$3x+7y$	$=$	$4$	Equation $1$
$2x+3y$	$=$	$1$	Equation $2$

Next, solve for $x$ in Equation

$2$ .

$2x+3y$	$=$	$1$
$2x+3y$ $-3y$	$=$	$1$ $-3y$	Subtract $3y$ from both sides
$2x$ $div2$	$=$	$(1-3y)$ $div2$	Divide both sides by $2$

$x$	$=$	$(1-3y)/2$	Simplify

Substitute $x$ into Equation

$1$ .

$3$ $x$ $+7y$	$=$	$4$	Equation $1$

$3$ $((1-3y)/2)$ $+7y$	$=$	$4$	$x=(1-3y)/2$

$\left(3\left(\frac{1-3y}{2}\right)\color{#CC0000}{\times2}\right)+(7y\color{#CC0000}{\times2})$	$=$	$4$ $times2$	Multiply all values by $2$

$3(1-3y)+14y$	$=$	$8$
$3-9y+14y$	$=$	$8$	Distribute $3$ inside the parenthesis
$3+5y$	$=$	$8$	Simplify
$3+5y$ $-3$	$=$	$8$ $-3$	Solve for $y$
$5y$	$=$	$5$
$5y$ $div5$	$=$	$5$ $div5$	Divide both sides by $5$
$y$	$=$	$1$

Now, substitute the value of $y$ into Equation

$2$

$2x+3$ $y$	$=$	$1$	Equation $2$
$2x+3$ $(1)$	$=$	$1$	$y=1$
$2x+3$ $-3$	$=$	$1$ $-3$	Subtract $3$ from both sides
$2x$ $div2$	$=$	$-2$ $div2$	Divide both sides by $2$
$x$	$=$	$-1$

$x=-1, y=1$

Question 16 of 18

Solve the following simultaneous equations by substitution.

$5a+2b=4$

$2a-3b=13$

$a=$ (2)

$b=$ (-3)

Incorrect

Help Video

Substitution Method

$1)$ make one variable the subject
$2)$ substitute into second equation
$3)$ solve the second equation
$4)$ substitute back

First, label the two equations

$1$ and

$2$ respectively.

$5a+2b$	$=$	$4$	Equation $1$
$2a-3b$	$=$	$13$	Equation $2$

Next, solve for $a$ in Equation

$2$ .

$2a-3b$	$=$	$13$
$2a-3b$ $+3b$	$=$	$13$ $+3b$	Add $3b$ to both sides
$2a$ $div2$	$=$	$(13+3b)$ $div2$	Divide both sides by $2$

$a$	$=$	$(13+3b)/2$	Simplify

Substitute $a$ into Equation

$1$ .

$5$ $a$ $+2b$	$=$	$4$	Equation $1$

$5$ $((13+3b)/2)$ $+2b$	$=$	$4$	$a=(13+3b)/2$

$\left(5\left(\frac{13+3b}{2}\right)\color{#CC0000}{\times2}\right)+(2b\color{#CC0000}{\times2})$	$=$	$4$ $times2$	Multiply all values by $2$

$5(13+3b)+4b$	$=$	$8$
$65+15b+4b$	$=$	$8$	Distribute $5$ inside the parenthesis
$65+19b$	$=$	$8$	Simplify
$65+19b$ $-65$	$=$	$8$ $-65$	Solve for $b$
$19b$	$=$	$-57$
$19b$ $div19$	$=$	$-57$ $div19$	Divide both sides by $19$
$b$	$=$	$-3$

Now, substitute the value of $b$ into Equation

$2$

$2a-3$ $b$	$=$	$13$	Equation $2$
$2a-3$ $(-3)$	$=$	$13$	$b=-3$
$2a+9$ $-9$	$=$	$13$ $-9$	Subtract $9$ from both sides
$2a$ $div2$	$=$	$4$ $div2$	Divide both sides by $2$
$a$	$=$	$2$

$a=2, b=-3$

Question 17 of 18

Solve the following simultaneous equations by substitution.

$4x-5y=14$

$2x+3y=-4$

$x=$ (1)

$y=$ (-2)

Incorrect

Help Video

Substitution Method

$1)$ make one variable the subject
$2)$ substitute into second equation
$3)$ solve the second equation
$4)$ substitute back

First, label the two equations

$1$ and

$2$ respectively.

$4x-5y$	$=$	$14$	Equation $1$
$2x+3y$	$=$	$-4$	Equation $2$

Next, solve for $x$ in Equation

$2$ .

$2x+3y$	$=$	$-4$
$2x+3y$ $-3y$	$=$	$-4$ $-3y$	Subtract $3y$ from both sides
$2x$ $div2$	$=$	$(-4-3y)$ $div2$	Divide both sides by $2$

$x$	$=$	$(-4-3y)/2$	Simplify

Substitute $x$ into Equation

$1$ .

$4$ $x$ $-5y$	$=$	$14$	Equation $1$

$4$ $((-4-3y)/2)$ $-5y$	$=$	$14$	$x=(-4-3y)/2$

$\left(4\left(\frac{-4-3y}{2}\right)\color{#CC0000}{\times2}\right)-(5y\color{#CC0000}{\times2})$	$=$	$14$ $times2$	Multiply all values by $2$

$4(-4-3y)-10y$	$=$	$28$
$-16-12y-10y$	$=$	$28$	Distribute $4$ inside the parenthesis
$-16-22y$	$=$	$28$	Simplify
$-16-22y$ $+16$	$=$	$28$ $+16$	Solve for $y$
$-22y$	$=$	$44$
$-22y$ $div-22$	$=$	$44$ $div-22$	Divide both sides by $-22$
$y$	$=$	$-2$

Now, substitute the value of $y$ into Equation

$2$

$2x+3$ $y$	$=$	$-4$	Equation $2$
$2x+3$ $(-2)$	$=$	$-4$	$y=-2$
$2x-6$ $+6$	$=$	$-4$ $+6$	Add $6$ to both sides
$2x$ $div2$	$=$	$2$ $div2$	Divide both sides by $2$
$x$	$=$	$1$

$x=1, y=-2$

Question 18 of 18

Solve the following simultaneous equations by substitution.

$7x-2y=6$

$3x+4y=22$

$x=$ (2)

$y=$ (4)

Incorrect

Help Video

Substitution Method

$1)$ make one variable the subject
$2)$ substitute into second equation
$3)$ solve the second equation
$4)$ substitute back

First, label the two equations

$1$ and

$2$ respectively.

$7x-2y$	$=$	$6$	Equation $1$
$3x+4y$	$=$	$22$	Equation $2$

Next, solve for $y$ in Equation

$1$ .

$7x-2y$	$=$	$6$
$7x-2y$ $+2y$	$=$	$6$ $+2y$	Add $2y$ to both sides
$7x$ $-6$	$=$	$6+2y$ $-6$	Subtract $2y$ from both sides
$(7x-6)$ $div2$	$=$	$2y$ $div2$	Divide both sides by $2$

$(7x-6)/2$	$=$	$y$	Simplify

$y$	$=$	$(7x-6)/2$	Simplify

Substitute $y$ into Equation

$2$ .

$3x+4$ $y$	$=$	$22$	Equation $2$

$3x+4$ $((7x-6)/2)$	$=$	$22$	$y=(7x-6)/2$

$(3x\color{#CC0000}{\times2})+\left(4\left(\frac{7x-6}{2}\right)\color{#CC0000}{\times2}\right)$	$=$	$22$ $times2$	Multiply all values by $2$

$6x+4(7x-6)$	$=$	$44$
$6x+28x-24$	$=$	$44$	Distribute $4$ inside the parenthesis
$34x-24$	$=$	$44$	Simplify
$34x-24$ $+24$	$=$	$44$ $+24$	Solve for $x$
$34x$	$=$	$68$
$34x$ $div34$	$=$	$68$ $div34$	Divide both sides by $34$
$x$	$=$	$2$

Now, substitute the value of $x$ into Equation

$1$

$7$ $x$ $-2y$	$=$	$6$	Equation $1$
$7$ $(2)$ $-2y$	$=$	$6$	$x=2$
$14-2y$ $-14$	$=$	$6$ $-14$	Subtract $14$ from both sides
$-2y$ $div-2$	$=$	$-8$ $div-2$	Divide both sides by $-2$
$y$	$=$	$4$

$x=2, y=4$

$4x-2$ $y$	$=$	$10$	Equation $2$
$4x-2$ $(7-2x)$	$=$	$11$	$y=7-2x$
$4x-14+4x$	$=$	$10$	Distribute $2$ inside the parenthesis
$8x-14$	$=$	$10$	Simplify
$8x-14$ $+14$	$=$	$10$ $+14$	Solve for $x$
$8x$	$=$	$24$
$8x$ $div8$	$=$	$24$ $div8$	Divide both sides by $8$
$x$	$=$	$3$

$3$ $x$ $-2y$	$=$	$20$	Equation $1$
$3$ $(-4-2y)$ $-2y$	$=$	$20$	$x=-4-2y$
$-12-6y-2y$	$=$	$20$	Distribute $3$ inside the parenthesis
$-12-8y$	$=$	$20$	Simplify
$-12-8y$ $+12$	$=$	$20$ $+12$	Solve for $y$
$-8y$	$=$	$32$
$-8y$ $div(-8)$	$=$	$32$ $div(-8)$	Divide both sides by $-8$
$y$	$=$	$-4$

$2a+5$ $b$	$=$	$10$	Equation $2$
$2a+5$ $(2a+2)$	$=$	$10$	$b=2a+2$
$2a+10a+10$	$=$	$10$	Distribute $5$ inside the parenthesis
$12a+10$	$=$	$10$	Simplify
$12a+10$ $-10$	$=$	$10$ $-10$	Solve for $a$
$12a$	$=$	$0$
$12a$ $div12$	$=$	$0$ $div12$	Divide both sides by $12$
$a$	$=$	$0$

$m-5n$	$=$	$10$
$m-5n$ $+5n$	$=$	$10$ $+5n$	Add $5n$ to both sides
$m$	$=$	$10+5n$	Simplify

$m-5$ $n$	$=$	$10$	Equation $1$
$m-5$ $(-1)$	$=$	$10$	$n=-1$
$m+5$ $-5$	$=$	$10$ $-5$	Subtract $5$ from both sides
$m$	$=$	$5$

$x-y$	$=$	$8$
$x-y$ $+y$	$=$	$8$ $+y$	Add $y$ to both sides
$x$	$=$	$8+y$	Simplify

$2$ $x$ $+y$	$=$	$1$	Equation $2$
$2$ $(8+y)$ $+y$	$=$	$1$	$x=8+y$
$16+2y+y$	$=$	$1$	Distribute $2$ inside the parenthesis
$16+3y$	$=$	$1$	Simplify
$16+3y$ $-16$	$=$	$1$ $-16$	Solve for $y$
$3y$	$=$	$-15$
$y$	$=$	$-5$	Divide both sides by $3$

$x-$ $y$	$=$	$8$	Equation $1$
$x-$ $(-5)$	$=$	$8$	$y=-5$
$x+5$	$=$	$8$
$x+5$ $-5$	$=$	$8$ $-5$	Simplify
$x$	$=$	$3$

$2x-y$	$=$	$6$
$2x-y$ $+y-6$	$=$	$6$ $+y-6$	Add $y-6$ to both sides
$2x-6$	$=$	$y$	Simplify
$y$	$=$	$2x-6$	Simplify

$x+3$ $y$	$=$	$10$	Equation $2$
$x+3$ $(2x-6)$	$=$	$10$	$y=2x-6$
$x+6x-18$	$=$	$10$	Distribute $3$ inside the parenthesis
$7x-18$	$=$	$10$	Simplify
$7x-18$ $+18$	$=$	$10$ $+18$	Solve for $x$
$7x$	$=$	$28$
$x$	$=$	$4$	Divide both sides by $7$

$2$ $x$ $-y$	$=$	$6$	Equation $1$
$2$ $(4)$ $-y$	$=$	$6$	$x=4$
$8-y$	$=$	$6$
$8-y$ $-8$	$=$	$6$ $-8$	Simplify
$-y$	$=$	$-2$
$y$	$=$	$2$

$2a+b$	$=$	$5$
$2a+b$ $-2a$	$=$	$5$ $-2a$	Subtract $2a$ from both sides
$b$	$=$	$5-2a$	Simplify

$5a-3$ $b$	$=$	$7$	Equation $2$
$5a-3$ $(5-2a)$	$=$	$7$	$b=5-2a$
$5a-15+6a$	$=$	$7$	Distribute $-3$ inside the parenthesis
$11a-15$	$=$	$7$	Simplify
$11a-15$ $+15$	$=$	$7$ $+15$	Solve for $a$
$11a$	$=$	$22$
$a$	$=$	$2$	Divide both sides by $11$

$2$ $a$ $+b$	$=$	$5$	Equation $1$
$2$ $(2)$ $+b$	$=$	$5$	$a=2$
$4+b$	$=$	$5$
$4+b$ $-4$	$=$	$5$ $-4$	Simplify
$b$	$=$	$1$

$x-y$	$=$	$2$
$x-y$ $+y$	$=$	$2$ $+y$	Add $y$ to both sides of the equation
$x$	$=$	$2+y$	Simplify

$2$ $x$ $+y$	$=$	$1$	Equation $1$
$2$ $(2+y)$ $+y$	$=$	$1$	$x=2+y$
$4+2y+y$	$=$	$1$	Distribute $2$ inside the parenthesis
$4+3y$	$=$	$1$	Simplify
$4+3y$ $-4$	$=$	$1$ $-4$	Solve for $y$
$3y$	$=$	$-3$
$y$	$=$	$-1$	Divide both sides by $3$

$x-$ $y$	$=$	$2$	Equation $2$
$x-$ $(-1)$	$=$	$2$	$y=-1$
$x+1$	$=$	$2$
$x+1$ $-1$	$=$	$2$ $-1$	Simplify
$x$	$=$	$1$

$x-y$	$=$	$1$
$x-y$ $+y$	$=$	$1$ $+y$	Add $y$ to both sides
$x$	$=$	$1+y$	Simplify

$x-$ $y$	$=$	$1$	Equation $1$
$x-$ $(3)$	$=$	$1$	$y=3$
$x-3$ $+3$	$=$	$1$ $+3$	Add $3$ to both sides
$x$	$=$	$4$

$2x+y$	$=$	$7$
$2x+y$ $-2x$	$=$	$7$ $-2x$	Subtract $2x$ from both sides
$y$	$=$	$7-2x$	Simplify

$2$ $x$ $+y$	$=$	$7$	Equation $1$
$2$ $(3)$ $+y$	$=$	$7$	$x=3$
$6+y$ $-6$	$=$	$7$ $-6$	Subtract $6$ from both sides
$y$	$=$	$1$

$2x+y$	$=$	$7$
$2(3)+1$	$=$	$7$	Substitute $x=3$ and $y=1$
$6+1$	$=$	$7$
$7$	$=$	$7$

$a-3b$	$=$	$2$
$a-3b$ $+3b$	$=$	$2$ $+3b$	Add $3b$ to both sides
$a$	$=$	$2+3b$	Simplify

$2$ $a$ $-b$	$=$	$14$	Equation $2$
$2$ $(2+3b)$ $-b$	$=$	$14$	$a=2+3b$
$4+6b-b$	$=$	$14$	Distribute $2$ inside the parenthesis
$5b+4$	$=$	$14$	Simplify
$5b+4$ $-4$	$=$	$14$ $-4$	Solve for $b$
$5b$	$=$	$10$
$5b$ $div5$	$=$	$10$ $div5$	Divide both sides by $5$
$b$	$=$	$2$

$a-3$ $b$	$=$	$2$	Equation $1$
$a-3$ $(2)$	$=$	$2$	$b=2$
$a-6$ $+6$	$=$	$2$ $+6$	Add $6$ to both sides
$a$	$=$	$8$

Substitution Method

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Quiz summary

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1. Question

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3. Question

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17. Question

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18. Question

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Substitution Method

Quizzes

$x+2y$	$=$	$-4$
$x+2y$ $-2y$	$=$	$-4$ $-2y$	Subtract $2y$ from both sides
$x$	$=$	$-4-2y$	Simplify

$x+2$ $y$	$=$	$-4$	Equation $2$
$x+2$ $(-2)$	$=$	$-4$	$y=-2$
$x-8$ $+8$	$=$	$-4$ $+8$	Add $8$ to both sides
$x$	$=$	$4$

$x-y$	$=$	$7$
$x-y$ $+y$	$=$	$7$ $+y$	Add $y$ from both sides
$x$	$=$	$7+y$	Simplify

$2$ $x$ $+5y$	$=$	$7$	Equation $1$
$2$ $(7+y)$ $+5y$	$=$	$7$	$x=7+y$
$14+2y+5y$	$=$	$7$	Distribute $2$ inside the parenthesis
$14+7y$	$=$	$7$	Simplify
$14+7y$ $-14$	$=$	$7$ $-14$	Solve for $y$
$7y$	$=$	$-7$
$7y$ $div7$	$=$	$-7$ $div7$	Divide both sides by $7$
$y$	$=$	$-1$

$a-b$	$=$	$5$
$a-b$ $+b$	$=$	$5$ $+b$	Add $b$ to both sides
$a$	$=$	$5+b$	Simplify

$2$ $a$ $+b$	$=$	$4$	Equation $2$
$2$ $(5+b)$ $+b$	$=$	$4$	$a=5+b$
$10+2b+b$	$=$	$4$	Distribute $2$ inside the parenthesis
$10+3b$	$=$	$4$	Simplify
$10+3b$ $-10$	$=$	$4$ $-10$	Solve for $b$
$3b$	$=$	$-6$
$3b$ $div3$	$=$	$-6$ $div3$	Divide both sides by $3$
$b$	$=$	$-2$

$a-$ $b$	$=$	$5$	Equation $1$
$a-$ $(-2)$	$=$	$5$	$b=2$
$a+2$	$=$	$5$	Simplify
$a+2$ $-2$	$=$	$5$ $-2$	Subtract $2$ from both sides
$a$	$=$	$3$

$b$	$=$	$2$ $a$ $+2$	Equation $1$
$b$	$=$	$2$ $(0)$ $+2$	$a=0$
$b$	$=$	$0+2$
$b$	$=$	$2$

$2$ $m$ $+5n$	$=$	$5$	Equation $1$
$2$ $(10+5n)$ $+5n$	$=$	$5$	$m=10+5n$
$20+10n+5n$	$=$	$5$	Distribute $2$ inside the parenthesis
$20+15n$	$=$	$5$	Simplify
$20+15n$ $-20$	$=$	$5$ $-20$	Solve for $n$
$15n$	$=$	$-15$
$15n$ $div15$	$=$	$-15$ $div15$	Divide both sides by $15$
$n$	$=$	$-1$

$4a+2b$	$=$	$4$
$(4a$ $div2$ $)+(2b$ $div2$ $)$	$=$	$4$ $div2$	Divide the values of both sides by $2$
$2a+b$ $-2a$	$=$	$2$ $-2a$	Subtract $2a$ from both sides
$b$	$=$	$2-2a$	Simplify