Question

use substitution to solve each system of equations.

1. ( x = 3 )

( -x + 5y = 7 )
(__ , __)

1. ( y = -4 )

( 4x - y = -8 )
(__ , __)

1. ( -2y = 6 )

( 6x + 9y = 9 )
(__ , __)

1. ( 2x = y )

( -8x + y = 24 )
(__ , __)

1. ( y = -x + 10 )

( 12x = y + 3 )
(__ , __)

1. ( y = 4x - 25 )

( 3x + y = 10 )
(__ , __)

1. ( x = 6y + 14 )

( x = 3y + 8 )
(__ , __)

1. ( y = x - 13 )

( y = -5x + 5 )
(__ , __)

1. ( -4x + y = 5 )

( 7x - 2y = -5 )
(__ , __)

1. ( 4x + y = 9 )

( 5x + 3y = -1 )
(__ , __)

1. ( 12x + 3y = -18 )

( -5x - 2y = 12 )
(__ , __)

1. ( 4x + 8y = -12 )

( 3x + 3y = 9 )
(__ , __)
education.com
find worksheets, games, lessons &...

Explanation:

Step1: Solve Problem 1

We have \( x = 3 \) and \( -x + 5y = 7 \). Substitute \( x = 3 \) into the second equation:
\( -3 + 5y = 7 \)
Add 3 to both sides: \( 5y = 7 + 3 = 10 \)
Divide by 5: \( y = \frac{10}{5} = 2 \)
So the solution is \( (3, 2) \).

Step2: Solve Problem 2

We have \( y = -4 \) and \( 4x - y = -8 \). Substitute \( y = -4 \) into the second equation:
\( 4x - (-4) = -8 \)
Simplify: \( 4x + 4 = -8 \)
Subtract 4: \( 4x = -8 - 4 = -12 \)
Divide by 4: \( x = \frac{-12}{4} = -3 \)
So the solution is \( (-3, -4) \).

Step3: Solve Problem 3

First, solve \( -2y = 6 \) for \( y \): \( y = \frac{6}{-2} = -3 \)
Now substitute \( y = -3 \) into \( 6x + 9y = 9 \):
\( 6x + 9(-3) = 9 \)
Simplify: \( 6x - 27 = 9 \)
Add 27: \( 6x = 9 + 27 = 36 \)
Divide by 6: \( x = \frac{36}{6} = 6 \)
So the solution is \( (6, -3) \).

Step4: Solve Problem 4

We have \( 2x = y \) and \( -8x + y = 24 \). Substitute \( y = 2x \) into the second equation:
\( -8x + 2x = 24 \)
Simplify: \( -6x = 24 \)
Divide by -6: \( x = \frac{24}{-6} = -4 \)
Then \( y = 2(-4) = -8 \)
So the solution is \( (-4, -8) \).

Step5: Solve Problem 5

We have \( y = -x + 10 \) and \( 12x = y + 3 \). Substitute \( y = -x + 10 \) into the second equation:
\( 12x = (-x + 10) + 3 \)
Simplify: \( 12x = -x + 13 \)
Add \( x \) to both sides: \( 13x = 13 \)
Divide by 13: \( x = 1 \)
Then \( y = -1 + 10 = 9 \)
So the solution is \( (1, 9) \).

Step6: Solve Problem 6

We have \( y = 4x - 25 \) and \( 3x + y = 10 \). Substitute \( y = 4x - 25 \) into the second equation:
\( 3x + (4x - 25) = 10 \)
Simplify: \( 7x - 25 = 10 \)
Add 25: \( 7x = 35 \)
Divide by 7: \( x = 5 \)
Then \( y = 4(5) - 25 = 20 - 25 = -5 \)
So the solution is \( (5, -5) \).

Step7: Solve Problem 7

We have \( x = 6y + 14 \) and \( x = 3y + 8 \). Set them equal:
\( 6y + 14 = 3y + 8 \)
Subtract \( 3y \): \( 3y + 14 = 8 \)
Subtract 14: \( 3y = 8 - 14 = -6 \)
Divide by 3: \( y = -2 \)
Then \( x = 3(-2) + 8 = -6 + 8 = 2 \)
So the solution is \( (2, -2) \).

Step8: Solve Problem 8

We have \( y = x - 13 \) and \( y = -5x + 5 \). Set them equal:
\( x - 13 = -5x + 5 \)
Add \( 5x \): \( 6x - 13 = 5 \)
Add 13: \( 6x = 18 \)
Divide by 6: \( x = 3 \)
Then \( y = 3 - 13 = -10 \)
So the solution is \( (3, -10) \).

Step9: Solve Problem 9

From \( -4x + y = 5 \), we get \( y = 4x + 5 \). Substitute into \( 7x - 2y = -5 \):
\( 7x - 2(4x + 5) = -5 \)
Simplify: \( 7x - 8x - 10 = -5 \)
\( -x - 10 = -5 \)
Add 10: \( -x = 5 \)
Multiply by -1: \( x = -5 \)
Then \( y = 4(-5) + 5 = -20 + 5 = -15 \)
So the solution is \( (-5, -15) \).

Step10: Solve Problem 10

From \( 4x + y = 9 \), we get \( y = 9 - 4x \). Substitute into \( 5x + 3y = -1 \):
\( 5x + 3(9 - 4x) = -1 \)
Simplify: \( 5x + 27 - 12x = -1 \)
\( -7x + 27 = -1 \)
Subtract 27: \( -7x = -28 \)
Divide by -7: \( x = 4 \)
Then \( y = 9 - 4(4) = 9 - 16 = -7 \)
So the solution is \( (4, -7) \).

Step11: Solve Problem 11

From \( 12x + 3y = -18 \), divide by 3: \( 4x + y = -6 \), so \( y = -4x - 6 \). Substitute into \( -5x - 2y = 12 \):
\( -5x - 2(-4x - 6) = 12 \)
Simplify: \( -5x + 8x + 12 = 12 \)
\( 3x + 12 = 12 \)
Subtract 12: \( 3x = 0 \)
Divide by 3: \( x = 0 \)
Then \( y = -4(0) - 6 = -6 \)
So the solution is \( (0, -6) \).

Step12: Solve Problem 12

Simplify the equations. Divide the first equation by 4: \( x + 2y = -3 \), so \( x = -3 - 2y \). Divide the second equation by 3: \( x + y = 3 \), so \( x = 3 - y \). Set equal:
\( -3 - 2y = 3 - y \)
Add \( 2y \): \( -3 = 3 + y \)
Subtract 3: \( y = -6 \)
Then \( x = 3 - (-6) = 9 \)
So the solution is \( (9, -6) \).

Answer:

1. \( (3, 2) \)
2. \( (-3, -4) \)
3. \( (6, -3) \)
4. \( (-4, -8) \)
5. \( (1, 9) \)
6. \( (5, -5) \)
7. \( (2, -2) \)
8. \( (3, -10) \)
9. \( (-5, -15) \)
10. \( (4, -7) \)
11. \( (0, -6) \)
12. \( (9, -6) \)