Question

n. clearly identify your solution.

1. \

$$\begin{cases} y = -3x + 5 \\\\ y = -8x + 25 \\end{cases}$$

1. \

$$\begin{cases} 2x - 3y = 9 \\\\ -5x - 3y = 30 \\end{cases}$$

\

$$\begin{cases} 2x - 3y = 14 \\\\ x + 3y = -11 \\end{cases}$$

\

$$\begin{cases} 6x + 5y = 4 \\\\ 6x - 7y = -20 \\end{cases}$$

Explanation:

Problem 2:

Step1: Set equations equal

Since both equal \( y \), set \( -3x + 5 = -8x + 25 \).

Step2: Solve for \( x \)

Add \( 8x \) to both sides: \( 5x + 5 = 25 \). Subtract 5: \( 5x = 20 \), so \( x = 4 \).

Step3: Find \( y \)

Substitute \( x = 4 \) into \( y = -3x + 5 \): \( y = -3(4) + 5 = -7 \).

Step1: Subtract equations

Subtract the first equation \( 2x - 3y = 9 \) from the second \( -5x - 3y = 30 \): \( (-5x - 3y) - (2x - 3y) = 30 - 9 \).

Step2: Simplify for \( x \)

Simplify: \( -7x = 21 \), so \( x = -3 \).

Step3: Find \( y \)

Substitute \( x = -3 \) into \( 2x - 3y = 9 \): \( 2(-3) - 3y = 9 \) → \( -6 - 3y = 9 \) → \( -3y = 15 \) → \( y = -5 \).

Step1: Add equations

Add \( 2x - 3y = 14 \) and \( x + 3y = -11 \): \( 3x = 3 \).

Step2: Solve for \( x \)

\( x = 1 \).

Step3: Find \( y \)

Substitute \( x = 1 \) into \( x + 3y = -11 \): \( 1 + 3y = -11 \) → \( 3y = -12 \) → \( y = -4 \).

Answer:

\( x = 4, y = -7 \)

Problem 4: