Question

solve the following system; show your work/process: \\(\

$$\begin{cases} y = 4x - 3 \\\\ y = -2x + 9 \\end{cases}$$

\\) solution: (\\_\\_\\_\\_\\_\\_, \\_\\_\\_\\_\\_\\_)

Explanation:

Step1: Set the two equations equal

Since \( y = 4x - 3 \) and \( y = -2x + 9 \), we can set \( 4x - 3 = -2x + 9 \).

Step2: Solve for x

Add \( 2x \) to both sides: \( 4x + 2x - 3 = -2x + 2x + 9 \), which simplifies to \( 6x - 3 = 9 \).
Then add 3 to both sides: \( 6x - 3 + 3 = 9 + 3 \), so \( 6x = 12 \).
Divide both sides by 6: \( x = \frac{12}{6} = 2 \).

Step3: Solve for y

Substitute \( x = 2 \) into \( y = 4x - 3 \): \( y = 4(2) - 3 = 8 - 3 = 5 \).

Answer:

(2, 5)