Question

y=x+6
y=-x+2
solve both and give intersecting points

Answer 1

To find the intersection points of the equations \( y = x + 6 \) and \( y = -x + 2 \), we can set the equations equal to each other:

\[
x + 6 = -x + 2
\]

Now, let’s solve for \( x \):

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

2. Subtract 6 from both sides:
\[
2x = 2 - 6
\]
\[
2x = -4
\]

3. Divide by 2:
\[
x = -2
\]

Now, substitute \( x = -2 \) back into one of the original equations to find \( y \). I'll use the first equation \( y = x + 6 \):

\[
y = -2 + 6
\]
\[
y = 4
\]

Thus, the intersection point of the two lines is:

\[
\boxed{(-2, 4)}
\]