Substitution Method 1

Topics

Precalculus

Systems of Equations

Substitution Method

Substitution Method 1

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Question 1 of 5

Solve the following systems of equations by substitution.

x - y = 8

$x-y=8$

2 x + y = 1

$2x+y=1$

$x =$ $x=$ (3)

$y =$ $y=$ (-5)

Question 2 of 5

Solve the following systems of equations by substitution.

2 a + b = 5

$2a+b=5$

5 a - 3 b = 7

$5a-3b=7$

$a =$ $a=$ (2)

$b =$ $b=$ (1)

Question 3 of 5

Solve the following systems of equations by substitution.

x - y = 1

$x-y=1$

2 x + y = 11

$2x+y=11$

$x =$ $x=$ (4)

$y =$ $y=$ (3)

Question 4 of 5

Solve the following systems of equations by substitution.

a - 3 b = 2

$a-3b=2$

2 a - b = 14

$2a-b=14$

$a =$ $a=$ (8)

$b =$ $b=$ (2)

Question 5 of 5

Solve the following systems of equations by substitution.

2 x + 5 y = 7

$2x+5y=7$

x - y = 7

$x-y=7$

$x =$ $x=$ (6)

$y =$ $y=$ (-1)

$x - y$ $x-y$	$=$ $=$	$8$ $8$	Equation $1$ $1$
$2 x + y$ $2x+y$	$=$ $=$	$1$ $1$	Equation $2$ $2$

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

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

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

$2 a + b$ $2a+b$	$=$ $=$	$5$ $5$	Equation $1$ $1$
$5 a - 3 b$ $5a-3b$	$=$ $=$	$7$ $7$	Equation $2$ $2$

Substitution Method 1

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Quiz summary

Information

1. Question

Hint

Great Work!

Substitution Method

2. Question

Hint

Keep Going!

3. Question

Hint

Great Work!

Substitution Method

4. Question

Hint

Keep Going!

Substitution Method

5. Question

Hint

Excellent!

Substitution Method

Substitution Method

Quizzes

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

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

$2$ $2$ $x$ $x$ $+ y$ $+y$	$=$ $=$	$11$ $11$	Equation $2$ $2$
$2$ $2$ $(1 + y)$ $(1+y)$ $+ y$ $+y$	$=$ $=$	$11$ $11$	$x = 1 + y$ $x=1+y$
$2 y + 2 + y$ $2y+2+y$	$=$ $=$	$11$ $11$	Distribute $2$ $2$ inside the parenthesis
$3 y + 2$ $3y+2$	$=$ $=$	$11$ $11$	Simplify
$3 y + 2$ $3y+2$ $- 2$ $-2$	$=$ $=$	$11$ $11$ $- 2$ $-2$	Solve for $y$ $y$
$3 y$ $3y$	$=$ $=$	$9$ $9$
$3 y$ $3y$ $\div 3$ $div3$	$=$ $=$	$9$ $9$ $\div 3$ $div3$	Divide both sides by $3$ $3$
$y$ $y$	$=$ $=$	$3$ $3$

$a - 3 b$ $a-3b$	$=$ $=$	$2$ $2$	Equation $1$ $1$
$2 a - b$ $2a-b$	$=$ $=$	$14$ $14$	Equation $2$ $2$

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

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

$2 x + 5 y$ $2x+5y$	$=$ $=$	$7$ $7$	Equation $1$ $1$
$x - y$ $x-y$	$=$ $=$	$7$ $7$	Equation $2$ $2$

$2$ $2$ $x$ $x$ $+ 5 y$ $+5y$	$=$ $=$	$7$ $7$	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 $7$
$y$	$=$	$-1$

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