Substitution Method 2

Topics

Algebra 2

Systems of Equations

Substitution Method

Substitution Method 2

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 5

Solve the following systems of equations by substitution.

2 x - y = 6

$2x-y=6$

x + 3 y = 10

$x+3y=10$

$x =$ $x=$ (4)

$y =$ $y=$ (2)

Question 2 of 5

Solve the following systems of equations by substitution.

2 x + y = 1

$2x+y=1$

x - y = 2

$x-y=2$

$x =$ $x=$ (1)

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

Question 3 of 5

Solve the following systems of equations by substitution.

2 x + y = 7

$2x+y=7$

4 x - 2 y = 10

$4x-2y=10$

$x =$ $x=$ (3)

$y =$ $y=$ (1)

Question 4 of 5

Solve the following systems of equations by substitution.

3 x - 2 y = 20

$3x-2y=20$

x + 2 y = - 4

$x+2y=-4$

$x =$ $x=$ (4)

$y =$ $y=$ (-4)

Question 5 of 5

Solve the following systems of equations by substitution.

a - b = 5

$a-b=5$

2 a + b = 4

$2a+b=4$

$a =$ $a=$ (3)

$b =$ $b=$ (-2)

$2 x - y$ $2x-y$	$=$ $=$	$6$ $6$	Equation $1$ $1$
$x + 3 y$ $x+3y$	$=$ $=$	$10$ $10$	Equation $2$ $2$

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

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

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

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

Substitution Method 2

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Correct!

2. Question

Hint

Fantastic!

3. Question

Hint

Correct!

Substitution Method

4. Question

Hint

Fantastic!

Substitution Method

5. Question

Hint

Nice Job!

Substitution Method

Quizzes

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

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

$2 x + y$ $2x+y$	$=$ $=$	$7$ $7$	Equation $1$ $1$
$4 x - 2 y$ $4x-2y$	$=$ $=$	$10$ $10$	Equation $2$ $2$

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

$3 x - 2 y$ $3x-2y$	$=$ $=$	$20$ $20$	Equation $1$ $1$
$x + 2 y$ $x+2y$	$=$ $=$	$- 4$ $-4$	Equation $2$ $2$

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

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

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

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

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