Question

solve each system by substitution.

1. $y = -5x - 8$

$y = 7x + 4$

1. $-2x - 5y = -22$

$y = -4x + 8$

1. $-4x + 6y = 14$

$y = -4x + 21$
solve each system by elimination.

1. $-5x + 6y = -40$

$5x - 8y = 10$

1. $-x + y = 3$

$-x + 6y = 3$

Explanation:

Problem 3:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we set \( -5x - 8 = 7x + 4 \).

Step2: Solve for \( x \)

Add \( 5x \) to both sides: \( -8 = 12x + 4 \).
Subtract 4 from both sides: \( -12 = 12x \).
Divide by 12: \( x = -1 \).

Step3: Find \( y \)

Substitute \( x = -1 \) into \( y = 7x + 4 \): \( y = 7(-1) + 4 = -7 + 4 = -3 \).

Step1: Substitute \( y \) into the first equation

Substitute \( y = -4x + 8 \) into \( -2x - 5y = -22 \):
\( -2x - 5(-4x + 8) = -22 \).

Step2: Solve for \( x \)

Distribute: \( -2x + 20x - 40 = -22 \).
Combine like terms: \( 18x - 40 = -22 \).
Add 40: \( 18x = 18 \).
Divide by 18: \( x = 1 \).

Step3: Find \( y \)

Substitute \( x = 1 \) into \( y = -4x + 8 \): \( y = -4(1) + 8 = 4 \).

Step1: Substitute \( y \) into the first equation

Substitute \( y = -4x + 21 \) into \( -4x + 6y = 14 \):
\( -4x + 6(-4x + 21) = 14 \).

Step2: Solve for \( x \)

Distribute: \( -4x - 24x + 126 = 14 \).
Combine like terms: \( -28x + 126 = 14 \).
Subtract 126: \( -28x = -112 \).
Divide by -28: \( x = 4 \).

Step3: Find \( y \)

Substitute \( x = 4 \) into \( y = -4x + 21 \): \( y = -4(4) + 21 = -16 + 21 = 5 \).

Answer:

\( x = -1, y = -3 \)

Problem 4: