Question

y=x+6
y=-x+2
solve each equation and give intersecting point

Answer 1

To find the intersection point of the two equations \( y = x + 6 \) and \( y = -x + 2 \), we can set the equations equal to each other since at the intersection point, both expressions for \( y \) are equal.

1. Set the equations equal:
\[
x + 6 = -x + 2
\]

2. Solve for \( x \):
- Add \( x \) to both sides:
\[
2x + 6 = 2
\]
- Subtract 6 from both sides:
\[
2x = 2 - 6
\]
\[
2x = -4
\]
- Divide by 2:
\[
x = -2
\]

3. Now, substitute \( x = -2 \) back into either original equation to find \( y \). We'll use \( y = x + 6 \):
\[
y = -2 + 6 = 4
\]

Therefore, the intersection point of the two equations is:
\[
\boxed{(-2, 4)}
\]