![To solve the system of equations:
1. Set the two equations equal to each other since both equal \( y \):
\[
2x + 42 = 8x
\]
2. Rearrange the equation to isolate \( x \):
\[
42 = 8x - 2x
\]
\[
42 = 6x
\]
3. Divide both sides by 6 to solve for \( x \):
\[
x = 7
\]
4. Substitute \( x = 7 \) back into either equation to find \( y \). Using \( y = 8x \):
\[
y = 8(7) = 56
\]
Thus, the solution to the system of equations is:
\[
(x, y) = (7, 56)
\]](https://theinternetioimages-f2htc2ggcrath6d7.z01.azurefd.net/$web/askai/2113993c-78c5-46b2-b1a9-d1e059b6011d.webp)
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You are given the system of equations: 1. \( y = 2x + 42 \) 2. \( y = 8x \) Set the two expressions for \( y \) equal to each other: \[ 2x + 42 = 8x \] Now solve for \( x \): Subtract \( 2x \) from both sides: \[ 42 = 8x - 2x \] \[ 42 = 6x \] Divide both sides by 6: \[ x = 7 \] Now substitute \( x = 7 \) into either equation to find \( y \). Let's use the second equation: \[ y = 8x = 8 \times 7 = 56 \] **Final Solution:** \[ \boxed{(x, y) = (7, 56)} \]
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