Answer: (3, 4)
Step-by-step explanation: Hello! To do this, you have to substitute one of the equations into the other. You know that in the first equation, y = -x + 7. Substitute -x+7 for y in the second equation. You now have -x + 7 = x + 1. Add x to both sides of the equation. -x + 7 + x = x + x + 1. You now have 7 = 2x + 1. Subtract 1 from both sides of the equation. You now have 6 = 2x. Divide both sides of the equation by 2. You now have 3 = x. The x-coordinate of where both linear equations intersect is 3. (3, y).
You now have to solve for the y-coordinate. To do this, look at your given equations. Subtract 2 from both sides of the second equation. You now have y - 1 = x. Substitute y-1 for x in the first equation. You now have y = -(y - 1) + 7. Simplify to get y = -y + 1 + 7. Add y to both sides of the equation. y + y = -y + y + 1 + 7. You now have 2y = 1 + 7. Add 1 + 7 to get 2y = 8. Divide both sides by 2 to get y = 4. You now know that the x-coordinate where both linear equations intersect is 3, and you know that the y-coordinate where both linear equations intersect is 4. Your answer is in the format of (x, y), which is (3, 4).