Question

solve the system of equations.
\\( y = 8x + 11 \\)
\\( y = 5x + 29 \\)
\\( x = \\)
\\( y = \\)

Explanation:

Step1: Set the two equations equal

Since both equations equal \( y \), we can set them equal to each other: \( 8x + 11 = 5x + 29 \)

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides: \( 8x - 5x + 11 = 29 \)
Simplify: \( 3x + 11 = 29 \)
Subtract 11 from both sides: \( 3x = 29 - 11 \)
\( 3x = 18 \)
Divide by 3: \( x = \frac{18}{3} = 6 \)

Step3: Find \( y \) using \( x = 6 \)

Substitute \( x = 6 \) into \( y = 8x + 11 \): \( y = 8(6) + 11 \)
Calculate: \( y = 48 + 11 = 59 \)

Answer:

\( x = 6 \)
\( y = 59 \)