Question: In Exercises 13-20, solve by graphing. (See Example) 13. \( y = -x + 7 \) \( y = x + 1 \) 15…

In Exercises 13-20, solve by graphing. (See Example)

13. \( y = -x + 7 \) \( y = x + 1 \)

14. \( y = \frac{1}{2}x + 2 \)

Solution

To solve the system of equations by graphing, we find the point where the two equations intersect. Given the system: \[ \begin{cases} y = -x + 7 & \\ y = x + 1 & \end{cases} \] To find the solution, we set the two equations equal to each other: \[ -x + 7 = x + 1 \] Add \(x\) to both sides: \[ 7 = 2x + 1 \] Subtract 1 from both sides: \[ 6 = 2x \] Divide both sides by 2: \[ x = 3 \] Substitute \(x = 3\) back into one of the original equations to solve for \(y\): \[ y = 3 + 1 = 4 \] So, the solution to the system of equations is: \(x = 3, y = 4\) The graphs of the lines intersect at the point \((3, 4)\).