Elimination Method

Question 1 of 21

Solve the following simultaneous equations by elimination.

2 x - 3 y = 3

$2x-3y=3$

4 x + 3 y = 15

$4x+3y=15$

$x =$ $x=$ (3)

$y =$ $y=$ (1)

Question 2 of 21

Solve the following simultaneous equations by elimination.

$3x+y=5$

$x+y=3$

$x=$ (1)

$y=$ (2)

Question 3 of 21

Solve the following simultaneous equations by elimination.

$2x-3y=8$

$x-y=3$

$x=$ (1)

$y=$ (-2)

Question 4 of 21

Solve the following simultaneous equations by elimination.

$5x+y=-6$

$x+2y=24$

$x=$ (-4)

$y=$ (14)

Question 5 of 21

Solve the following simultaneous equations by elimination.

$5x+2y=25$

$4x-3y=-3$

$x=$ (3)

$y=$ (5)

Question 6 of 21

Solve the following simultaneous equations by elimination.

$3a-4b=24$

$4a-2b=12$

$a=$ (0)

$b=$ (-6)

Question 7 of 21

Solve the following simultaneous equations by elimination.

$2x-7y=19$

$x+2y=4$

$x=$ (6)

$y=$ (-1)

Question 8 of 21

Solve the following simultaneous equations by elimination.

$a-5b=8$

$2a-3b=9$

$x=$ (3)

$y=$ (-1)

Question 9 of 21

Solve the following simultaneous equations by elimination.

$2x+y=-5$

$4x-3y=5$

$x=$ (-1)

$y=$ (-3)

Question 10 of 21

Solve the following simultaneous equations by elimination.

$3x-5y=11$

$2x-y=5$

$x=$ (2)

$y=$ (-1)

Question 11 of 21

Solve the following simultaneous equations by elimination.

$2x-4y=-4$

$3x-2y=-10$

$x=$ (-4)

$y=$ (-1)

Question 12 of 21

Solve the following simultaneous equations by elimination.

$2x+3y=3$

$4x-2y=14$

$x=$ (3)

$y=$ (-1)

Question 13 of 21

Solve the following simultaneous equations by elimination.

$4x-3y=7$

$5x+2y=3$

$x=$ (1)

$y=$ (-1)

Question 14 of 21

Solve the following simultaneous equations by elimination.

$3x+2y=8$

$6x+8y=20$

$x=$ (2)

$y=$ (1)

Question 15 of 21

Solve the following simultaneous equations by elimination.

$2m+3n=18$

$4m-2n=12$

Write mixed numbers in the format “a b/c”

$x=$ (4 1/2)

$y=$ (3)

Question 16 of 21

Solve the following simultaneous equations by elimination.

$3x+5y=6$

$3x-2y=-1$

Write fractions in the format “a/b”

$x=$ (1/3)

$y=$ (1)

Question 17 of 21

Solve the following simultaneous equations by elimination.

$6x-y=-2$

$-18x+3y=4$

1. $x=-1,y=3$
2. $\text(Infinite Solutions)$
3. $x=2,y=-4$
4. $\text(No Solution)$

Question 18 of 21

Solve the following simultaneous equations by elimination.

$5x+2y=-3$

$-10x-4y=6$

1. $\text(No Solution)$
2. $\text(Infinite Solutions)$
3. $x=-2,y=-1$
4. $x=-1,y=2$

Question 19 of 21

Solve the following simultaneous equations by elimination.

$2x-3y=5$

$4x-6y=14$

1. $\text(No Solution)$
2. $\text(Infinite Solutions)$
3. $x=3,y=2$
4. $x=2,y=-3$

Question 20 of 21

Solve the following simultaneous equations by elimination.

$a/4+b=6$

$a/6+2b=8$

$a=$ (12)

$b=$ (3)

Incorrect

Help Video

Elimination Method

$1)$ make sure a variable has same coefficients on the 2 equations
$2)$ add or subtract the equations so that one variable is cancelled
$3)$ solve for the variable that remains
$4)$ substitute known value to one of the equations to solve for the other variable

First, label the two equations

$1$ and

$2$ respectively.

$a/4+b$	$=$	$6$	Equation $1$

$a/6+2b$	$=$	$8$	Equation $2$

Next, multiply the values of equation

$1$ by

$4$ and label the product as equation

$3$ .

$a/4+b$	$=$	$6$	Equation $1$

$\left(\frac{a}{4}+b\right)\color{#CC0000}{\times4}$	$=$	$6$ $times4$	Multiply the values of both sides by $4$ to cancel the fraction

$a+4b$	$=$	$24$	Equation $3$

Also multiply the values of equation

$2$ by

$6$ and label the product as equation

$4$ .

$a/6+2b$	$=$	$8$	Equation $2$

$\left(\frac{a}{6}+2b\right)\color{#CC0000}{\times6}$	$=$	$8$ $times6$	Multiply the values of both sides by $6$ to cancel the fraction
$a+12b$	$=$	$48$	Equation $4$

Then, subtract equation

$4$ from equation

$3$ .

$a+4b$	$=$	$24$
$-$ $(a+12b)$	$=$	$48$

$-8b$	$=$	$-24$	$a-a$ cancels out

Solve for $b$ from the difference.

$-8b$	$=$	$-24$
$-8b$ $div(-8)$	$=$	$-24$ $div(-8)$	Divide both sides by $-8$
$b$	$=$	$3$

Now, substitute the value of $b$ into any of the four equations.

$a+4$ $b$	$=$	$24$	Equation $3$
$a+4$ $(3)$	$=$	$24$	$b=3$
$a+12$ $-12$	$=$	$24$ $-12$	Subtract $12$ from both sides
$a$	$=$	$12$

$a=12, b =3$

Question 21 of 21

Solve the following simultaneous equations by elimination.

$x+y/2=5$

$(x+4y)/3=4$

$x=$ (4)

$y=$ (2)

Incorrect

Help Video

Elimination Method

$1)$ make sure a variable has same coefficients on the 2 equations
$2)$ add or subtract the equations so that one variable is cancelled
$3)$ solve for the variable that remains
$4)$ substitute known value to one of the equations to solve for the other variable

First, label the two equations

$1$ and

$2$ respectively.

$x+y/2$	$=$	$5$	Equation $1$

$(x+4y)/3$	$=$	$4$	Equation $2$

Next, multiply the values of equation

$1$ by

$2$ and label the product as equation

$3$ .

$x+y/2$	$=$	$5$	Equation $1$

$\left(x+\frac{y}{2}\right)\color{#CC0000}{\times2}$	$=$	$5$ $times2$	Multiply the values of both sides by $2$ to cancel the fraction

$2x+y$	$=$	$10$	Equation $3$

Also multiply the values of equation

$2$ by

$3$ and label the product as equation

$4$ .

$(x+4y)/3$	$=$	$4$	Equation $2$

$\left(\frac{x+4y}{3}\right)\color{#CC0000}{\times3}$	$=$	$4$ $times3$	Multiply the values of both sides by $3$ to cancel the fraction
$x+4y$	$=$	$12$	Equation $4$

Now multiply the values of equation

$4$ by

$2$ and label the product as equation

$5$ .

$x+4y$	$=$	$12$	Equation $4$

$(x+4y)$ $times2$	$=$	$12$ $times2$	Multiply the values of both sides by $2$
$2x+8y$	$=$	$24$	Equation $5$

Then, subtract equation

$3$ from equation

$5$ .

$2x+8y$	$=$	$24$
$-$ $(2x+y)$	$=$	$10$

$7y$	$=$	$14$	$2x-2x$ cancels out

Solve for $y$ from the difference.

$7y$	$=$	$14$
$7y$ $div7$	$=$	$14$ $div7$	Divide both sides by $7$
$y$	$=$	$2$

Now, substitute the value of $y$ into any of the five equations.

$2x+$ $y$	$=$	$10$	Equation $3$
$2x+$ $(2)$	$=$	$10$	$y=2$
$2x+2$ $-2$	$=$	$10$ $-2$	Subtract $2$ from both sides
$2x$ $div2$	$=$	$8$ $div2$	Divide both sides by $2$
$x$	$=$	$4$

$x=4, y =2$

$2 x - 3 y$ $2x-3y$	$=$ $=$	$3$ $3$	Equation $1$ $1$
$4 x + 3 y$ $4x+3y$	$=$ $=$	$15$ $15$	Equation $2$ $2$

$2 x - 3 y$ $2x-3y$	$=$ $=$	$3$ $3$
$4 x + 3 y$ $4x+3y$	$=$ $=$	$15$ $15$

$6 x$ $6x$	$=$ $=$	$18$ $18$	$- 3 y + 3 y$ $-3y+3y$ cancels out

$6 x$ $6x$	$=$ $=$	$18$ $18$
$x$ $x$	$=$ $=$	$3$ $3$	Divide both sides by $6$ $6$

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

$5x+y$	$=$	$-6$
$(5x+y)$ $xx 2$	$=$	$-6$ $xx 2$
$10x+2y$	$=$	$-12$	Simplify

$3x+y$	$=$	$5$
$-$ $(x+y)$	$=$	$3$

$2x$	$=$	$2$	$y-y$ cancels out

$2x$	$=$	$2$
$2x$ $div2$	$=$	$2$ $div2$	Divide both sides by $2$
$x$	$=$	$1$

$x$ $+y$	$=$	$3$	Equation $2$
$1$ $+y$	$=$	$3$	$x=1$
$1+y$ $-1$	$=$	$3$ $-1$	Subtract $1$ from both sides
$y$	$=$	$2$

$x-y$	$=$	$3$	Equation $2$
$(x-y)$ $times2$	$=$	$3$ $times2$	Multiply the values of both sides by $2$
$2x-2y$	$=$	$6$	Equation $3$

$2x-3y$	$=$	$8$
$-$ $(2x-2y)$	$=$	$6$

$-y$	$=$	$2$	$2x-2x$ cancels out

$-y$	$=$	$2$
$-y$ $div(-1)$	$=$	$2$ $div(-1)$	Divide both sides by $-1$
$y$	$=$	$-2$

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

$10x+2y$	$=$	$-12$
$x+2y$	$=$	$24$

$9x$	$=$	$-36$	$2y-2y$ cancels out

$x$ $+2y$	$=$	$24$	Equation $2$
$-4$ $+2y$	$=$	$24$	$x=-4$
$-4+2y$ $+4$	$=$	$24$ $+4$	Add $4$ to both sides
$2y$	$=$	$28$
$y$	$=$	$14$	Divide both sides by $2$

$5x+2y$	$=$	$25$
$(5x+2y)$ $xx 3$	$=$	$25$ $xx 3$
$15x+6y$	$=$	$75$	Simplify

$4x-14y$	$=$	$38$
$7x+14y$	$=$	$28$

$11x$	$=$	$66$	$-14y+14y$ cancels out

$4x-3y$	$=$	$-3$
$(4x-3y)$ $xx 2$	$=$	$-3$ $xx 2$
$8x-6y$	$=$	$-6$	Simplify

$5$ $x$ $+2y$	$=$	$25$	Equation $1$
$5$ $(3)$ $+2y$	$=$	$25$	$x=3$
$15+2y$	$=$	$25$
$15+2y$ $-15$	$=$	$25$ $-15$	Subtract $15$ from both sides
$2y$	$=$	$10$
$y$	$=$	$5$	Divide both sides by $2$

$4a-2b$	$=$	$12$
$(4a-2b)$ $xx 2$	$=$	$12$ $xx 2$
$8a-4b$	$=$	$24$	Simplify

$8a-4b$	$=$	$24$
$3a-4b$	$=$	$24$

$5a$	$=$	$0$	$-4b-(-4b)$ cancels out

$3$ $a$ $-4b$	$=$	$24$	Equation $1$
$3$ $(0)$ $-4b$	$=$	$24$	$a=0$
$-4b$	$=$	$24$
$b$	$=$	$-6$	Divide both sides by $-4$

$2x-7y$	$=$	$19$
$(2x-7y)$ $xx 2$	$=$	$19$ $xx 2$
$4x-14y$	$=$	$38$	Simplify

$x+2y$	$=$	$4$
$(x+2y)$ $xx 7$	$=$	$4$ $xx 7$
$7x+14y$	$=$	$28$	Simplify

$2$ $x$ $-7y$	$=$	$19$	Equation $1$
$2$ $(6)$ $-7y$	$=$	$19$	$x=6$
$12-7y$	$=$	$19$
$12-7y$ $-12$	$=$	$19$ $-12$	Subtract $12$ from both sides
$-7y$	$=$	$7$
$y$	$=$	$-1$	Divide both sides by $-7$

$a-5b$	$=$	$8$	Equation $1$
$(a-5b)$ $times2$	$=$	$8$ $times2$	Multiply the values of both sides by $2$
$2a-10b$	$=$	$16$	Equation $3$

$2a-10b$	$=$	$16$
$-$ $(2a-3b)$	$=$	$9$

$-7b$	$=$	$7$	$2a-2a$ cancels out

Elimination Method

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21. Question

$-7b$	$=$	$7$
$-7b$ $div(-7)$	$=$	$7$ $div(-7)$	Divide both sides by $-7$
$b$	$=$	$-1$

$a-5$ $b$	$=$	$8$	Equation $1$
$a-5$ $(-1)$	$=$	$8$	$b=-1$
$a+5$ $-5$	$=$	$8$ $-5$	Subtract $5$ from both sides
$a$	$=$	$3$

$2x+y$	$=$	$-5$	Equation $1$
$(2x+y)$ $times3$	$=$	$-5$ $times3$	Multiply the values of both sides by $3$
$6x+3y$	$=$	$-15$	Equation $3$

$4x-3y$	$=$	$5$
$+$ $(6x+3y)$	$=$	$-15$

$10x$	$=$	$-10$	$-3y+3y$ cancels out

$10x$	$=$	$-10$
$10x$ $div10$	$=$	$-10$ $div10$	Divide both sides by $10$
$x$	$=$	$-1$

$4$ $x$ $-3y$	$=$	$5$	Equation $2$
$4$ $(-1)$ $-3y$	$=$	$5$	$x=-1$
$-4-3y$ $+4$	$=$	$5$ $+4$	Add $4$ to both sides
$-3y$ $div(-3)$	$=$	$9$ $div(-3)$	Divide both sides by $-3$
$y$	$=$	$-3$

$2x-y$	$=$	$5$	Equation $2$
$(2x-y)$ $times5$	$=$	$5$ $times5$	Multiply the values of both sides by $5$
$10x-5y$	$=$	$25$	Equation $3$

$10x-5y$	$=$	$25$
$-$ $(3x-5y)$	$=$	$11$

$7x$	$=$	$14$	$-5y-(-5y)$ cancels out

$7x$	$=$	$14$
$7x$ $div7$	$=$	$14$ $div7$	Divide both sides by $7$
$x$	$=$	$2$

$3$ $x$ $-5y$	$=$	$11$	Equation $1$
$3$ $(2)$ $-5y$	$=$	$11$	$x=2$
$6-5y$ $-6$	$=$	$11$ $-6$	Subtract $6$ from both sides
$-5y$ $div(-5)$	$=$	$5$ $div(-5)$	Divide both sides by $-5$
$y$	$=$	$-1$