Question

solving systems by elimination (day 1)
e document! **
. clearly identify your solution.

1. $\

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

$

Explanation:

Step1: Set the two equations equal

Since both equations equal \( y \), we can set them equal to each other: \( -3x + 5 = -8x + 25 \)

Step2: Solve for \( x \)

Add \( 8x \) to both sides: \( -3x + 8x + 5 = 25 \) → \( 5x + 5 = 25 \)
Subtract 5 from both sides: \( 5x = 25 - 5 \) → \( 5x = 20 \)
Divide by 5: \( x = \frac{20}{5} = 4 \)

Step3: Find \( y \)

Substitute \( x = 4 \) into \( y = -3x + 5 \): \( y = -3(4) + 5 = -12 + 5 = -7 \)

Answer:

The solution to the system is \( x = 4 \), \( y = -7 \) (or the ordered pair \( (4, -7) \))