Question

Question was provided via image upload.

Explanation:

Step1: Solve System 1

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

Step2: Solve System 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: \( 4x = -12 \)
Divide by 4: \( x = -3 \)
So the solution is \( (-3, -4) \).

Step3: Solve System 3

We have \( -2y = 6 \) and \( 6x + 9y = 9 \). First, solve \( -2y = 6 \) for \( y \):
Divide by -2: \( y = -3 \)
Substitute \( y = -3 \) into \( 6x + 9y = 9 \):
\( 6x + 9(-3) = 9 \)
Simplify: \( 6x - 27 = 9 \)
Add 27: \( 6x = 36 \)
Divide by 6: \( x = 6 \)
So the solution is \( (6, -3) \).

Step4: Solve System 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: \( x = -4 \)
Then \( y = 2(-4) = -8 \)
So the solution is \( (-4, -8) \).

Step5: Solve System 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 System 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 \( y = 4(5) - 25 = -5 \)
So the solution is \( (5, -5) \).

Step7: Solve System 7

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

Step8: Solve System 8

We have \( y = x - 13 \) and \( y = -5x + 5 \). Set the two expressions for \( y \) 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 System 9

We have \( -4x + y = 5 \) (so \( y = 4x + 5 \)) and \( 7x - 2y = -5 \). Substitute \( y = 4x + 5 \) into the second equation:
\( 7x - 2(4x + 5) = -5 \)
Simplify: \( 7x - 8x - 10 = -5 \)
Combine like terms: \( -x - 10 = -5 \)
Add 10: \( -x = 5 \)
Multiply by -1: \( x = -5 \)
Then \( y = 4(-5) + 5 = -15 \)
So the solution is \( (-5, -15) \).

Step10: Solve System 10

We have \( 4x + y = 9 \) (so \( y = 9 - 4x \)) and \( 5x + 3y = -1 \). Substitute \( y = 9 - 4x \) into the second equation:
\( 5x + 3(9 - 4x) = -1 \)
Simplify: \( 5x + 27 - 12x = -1 \)
Combine like terms: \( -7x + 27 = -1 \)
Subtract 27: \( -7x = -28 \)
Divide by -7: \( x = 4 \)
Then \( y = 9 - 4(4) = -7 \)
So the solution is \( (4, -7) \).

Step11: Solve System 11

We have \( 12x + 3y = -18 \) (divide by 3: \( 4x + y = -6 \), so \( y = -4x - 6 \)) and \( -5x - 2y = 12 \). Substitute \( y = -4x - 6 \) into the second equation:
\( -5x - 2(-4x - 6) = 12 \)
Simplify: \( -5x + 8x + 12 = 12 \)
Combine like terms: \( 3x + 12 = 12 \)
Subtract 12: \( 3x = 0 \)
Divide by 3: \( x = 0 \)
Then \( y = -4(0) - 6 = -6 \)
So the solution is \( (0, -6) \).

Step12: Solve System 12

We have \( 4x + 8y = -12 \) (divide by 4: \( x + 2y = -3 \), so \( x = -3 - 2y \)) and \( 3x + 3y = 9 \) (divide by 3: \( x + y = 3 \)). Substitute \( x = -3 - 2y \) into \( x + y = 3 \):
\( -3 - 2y + y = 3 \)
Simplify: \( -3 - y = 3 \)
Add 3: \( -y = 6 \)
Multiply by -1: \( y = -6 \)
Then \( x = -3 - 2(-6) = 9 \)
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. \( (9, -6) \)