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To solve the simultaneous equations using the graph and by substitution:

**Equations:**
\[ y = 2x + 5 \]
\[ y = -x + 8 \]

### Part (a)
Use the diagram to find the solution graphically:
1. Look at the intersection point of the two lines on the graph.
2. From the graph, the lines intersect at \( (1, 7) \).

So, the solution to the simultaneous equations is \( x = 1 \) and \( y = 7 \).

### Part (b)
Now, substitute \( x = 1 \) into each equation and solve for \( y \).

**Substitute into the first equation:**
\[ y = 2(1) + 5 \]
\[ y = 2 + 5 \]
\[ y = 7 \]

**Substitute into the second equation:**
\[ y = -1 + 8 \]
\[ y = 7 \]

### Observations:
i) The value of \( y \) in each equation is the same (7).
ii) The value of \( y \) is consistent with the solution obtained graphically in part (a).

Do you have any questions or need more details? Here are some additional questions you might find useful:

1. How do you solve simultaneous equations algebraically?
2. What is the significance of the intersection point of two lines in a system of equations?
3. How can you verify the solution to simultaneous equations?
4. What are some common methods to solve simultaneous equations?
5. How do you interpret the solution of a system of equations graphically?

**Tip:** Always verify your solutions to simultaneous equations by substituting the values back into the original equations to ensure they satisfy both equations.

Learn how to solve simultaneous equations using graphical and substitution methods. This problem demonstrates the process step-by-step, covering key concepts such as simultaneous equations, graphical solution, and substitution method. Suitable for students in Grades 8-10.

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