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y=x+6

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

1 answer

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:

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