Question

y = –x + 4
y = 2x − 2

Answer 1

To find the intersection of the two lines given by the equations \( y = -x + 4 \) and \( y = 2x - 2 \), we can set the two equations equal to each other:

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

Now, we'll solve for \( x \):

1. Add \( x \) to both sides:

\[
4 = 3x - 2
\]

2. Add \( 2 \) to both sides:

\[
6 = 3x
\]

3. Divide by \( 3 \):

\[
x = 2
\]

Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). We'll use the first equation:

\[
y = -x + 4 = -2 + 4 = 2
\]

So, the intersection point of the two lines is:

\[
(x, y) = (2, 2)
\]

Thus, the solution is \( (2, 2) \).