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Question

Review the graphs of a system of these two linear equations in two variables: y=4x−10 and y=−2x+8 Find the solution of the system.

(1 point)
The solution of the system of equations is ().

Answer 1

To find the solution of the system of equations given by \( y = 4x - 10 \) and \( y = -2x + 8 \), we need to set the equations equal to each other:

\[ 4x - 10 = -2x + 8 \]

Now, let's solve for \( x \):

1. Add \( 2x \) to both sides: \[ 4x + 2x - 10 = 8 \] \[ 6x - 10 = 8 \]

2. Add \( 10 \) to both sides: \[ 6x = 18 \]

3. Divide by \( 6 \): \[ x = 3 \]

Now, substitute \( x = 3 \) back into one of the original equations to find \( y \). We'll use \( y = 4x - 10 \):

\[ y = 4(3) - 10 \] \[ y = 12 - 10 \] \[ y = 2 \]

Thus, the solution to the system of equations is:

\[ \boxed{(3, 2)} \]