Substitution Method 3

Topics

Algebra 2

Systems of Equations

Substitution Method

Substitution Method 3

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Question 1 of 4

Solve the following systems of equations by substitution.

$8a+5b=6$

$4a+2b=4$

$a=$ (2)

$b=$ (-2)

Question 2 of 4

Solve the following systems of equations by substitution.

$2x+5y=17$

$3x+3y=12$

$x=$ (1)

$y=$ (3)

Question 3 of 4

Solve the following systems of equations by substitution.

$3x+7y=4$

$2x+3y=1$

$x=$ (-1)

$y=$ (1)

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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 4 of 4

Solve the following systems of equations by substitution.

$5a+2b=4$

$2a-3b=13$

$a=$ (2)

$b=$ (-3)

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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 $2$
$a$	$=$	$2$

$a=2, b=-3$

$8a+5$ $b$	$=$	$6$	Equation $1$
$8a+5$ $(2-2a)$	$=$	$6$	$b=2-2a$
$8a+10-10a$	$=$	$6$	Distribute $5$ inside the parenthesis
$10-2a$	$=$	$6$	Simplify
$10-2a$ $-10$	$=$	$6$ $-10$	Solve for $a$
$-2a$	$=$	$-4$
$-2a$ $div(-2)$	$=$	$-4$ $div(-2)$	Divide both sides by $-2$
$a$	$=$	$2$

$3x+3y$	$=$	$12$
$(3x$ $div3$ $)+(3y$ $div3$ $)$	$=$	$12$ $div3$	Divide the values of both sides by $3$
$x+y$ $-y$	$=$	$4$ $-y$	Subtract $y$ from both sides
$x$	$=$	$4-y$	Simplify

$3x+3$ $y$	$=$	$12$	Equation $2$
$3x+3$ $(3)$	$=$	$12$	$y=3$
$3x+9$ $-9$	$=$	$12$ $-9$	Subtract $9$ to both sides
$3x$ $div3$	$=$	$3$ $div3$	Divide both sides by $3$
$x$	$=$	$1$

Substitution Method 3

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Quiz summary

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1. Question

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Keep Going!

Substitution Method

2. Question

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Excellent!

Substitution Method

3. Question

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Correct!

Substitution Method

4. Question

Hint

Nice Job!

Substitution Method

Quizzes

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

$4$ $a$ $+2b$	$=$	$4$	Equation $1$
$4$ $(2)$ $+2b$	$=$	$4$	$a=2$
$8+2b$ $-8$	$=$	$4$ $-8$	Subtract $8$ from both sides
$2b$ $div2$	$=$	$-4$ $div2$	Divide both sides by $2$
$b$	$=$	$-2$

$2$ $x$ $+5y$	$=$	$17$	Equation $1$
$2$ $(4-y)$ $+5y$	$=$	$17$	$x=4-y$
$8-2y+5y$	$=$	$17$	Distribute $2$ inside the parenthesis
$8+3y$	$=$	$17$	Simplify
$8+3y$ $-8$	$=$	$17$ $-8$	Solve for $y$
$3y$	$=$	$9$
$3y$ $div3$	$=$	$9$ $div3$	Divide both sides by $3$
$y$	$=$	$3$