Question

solve the system of equations.
y=9x+13
y=2x+48
x =
y =

Explanation:

Step1: Set the two equations equal

Since both equations equal \( y \), we can set \( 9x + 13 = 2x + 48 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 9x - 2x + 13 = 48 \), which simplifies to \( 7x + 13 = 48 \). Then subtract 13 from both sides: \( 7x = 48 - 13 = 35 \). Divide both sides by 7: \( x = \frac{35}{7} = 5 \).

Step3: Solve for \( y \)

Substitute \( x = 5 \) into one of the original equations, say \( y = 9x + 13 \). Then \( y = 9(5) + 13 = 45 + 13 = 58 \).

Answer:

\( x = 5 \)
\( y = 58 \)