Question

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.

(2 points)

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Answer 1

To find the solution of the system of equations given by \( y = 4x - 10 \) and \( y = -2x + 8 \), we can set the two equations equal to each other since they both equal \( y \).

1. Set the equations equal to each other:
\[
4x - 10 = -2x + 8
\]

2. Now, solve for \( x \). First, add \( 2x \) to both sides:
\[
4x + 2x - 10 = 8
\]
\[
6x - 10 = 8
\]

3. Next, add \( 10 \) to both sides:
\[
6x = 18
\]

4. Now, divide by \( 6 \):
\[
x = 3
\]

5. Now that we have \( x \), substitute back into one of the equations to find \( y \). We'll use the second equation for this:
\[
y = -2(3) + 8
\]
\[
y = -6 + 8
\]
\[
y = 2
\]

The solution to the system of equations is \( (x, y) = (3, 2) \).

Thus, the solution of the system is:
\[
\boxed{(3, 2)}
\]