Answer: In summary, the solution is \((x, y) = (1, 1)\).
Step-by-step explanation:
Let's solve the system of equations by graphing:
1. **Equation 1**: \(y = 2x + 2\)
2. **Equation 2**: \(y = x\)
First, let's find the **x-intercept** for each equation:
1. For Equation 1:
- Set \(y\) to 0: \(0 = 2x + 2\)
- Solve for \(x\): \(x = -1\)
2. For Equation 2:
- Set \(y\) to 0: \(0 = x\)
- Solve for \(x\): \(x = 0\)
Now, let's find the **y-intercept** for each equation:
1. For Equation 1:
- Set \(x\) to 0: \(y = 2(0) + 2\)
- Solve for \(y\): \(y = 2\)
2. For Equation 2:
- Set \(x\) to 0: \(y = 0\)
Next, let's graph both equations on the same coordinate system:
- Equation 1 (red line): \(y = 2x + 2\)
- Equation 2 (blue line): \(y = x\)
The lines intersect at the point \((1, 1)\). Therefore, the solution to the system of equations is \(x = 1\) and \(y = 1\).
In summary, the solution is \((x, y) = (1, 1)\).
