The problem involves solving the system of simultaneous equations by finding the intersection point of the two lines shown in the graph:

1. $y = -2x + 7$
2. $y = \frac{1}{2}x + 1$

To solve graphically, observe the point where the two lines meet.

From the graph:

The two lines intersect at the point $(2, 2)$. This means:

• $x = 2$
• $y = 2$

Verification:

We can substitute $x = 2$ into both equations to verify:

1. In $y = -2x + 7$: $y = -2(2) + 7 = -4 + 7 = 2$

2. In $y = \frac{1}{2}x + 1$: $y = \frac{1}{2}(2) + 1 = 1 + 1 = 2$

Both equations give $y = 2$, confirming that the solution is correct. Therefore, the solution to the system of equations is: $\boxed{(2, 2)}$

Would you like a deeper explanation, or do you have further questions?

Here are five related questions to explore:

1. How can you algebraically solve the same system of equations?
2. What does the slope of each line tell us about their orientation on the graph?
3. How would the solution change if the two lines were parallel?
4. What is the importance of the y-intercept in these equations?
5. How can graphing software or a calculator be used to find solutions to simultaneous equations?

Tip: To solve simultaneous equations algebraically, equate the two equations and solve for $x$, then substitute $x$ back to find $y$.