Let's solve the problem step-by-step.

Part (a)

We need to find the point of intersection of the lines $y = 2x + 5$ and $x = 2$. The diagram shows these two lines intersecting, and we know the point of intersection will have an $x$-coordinate of $x = 2$, as one of the equations is $x = 2$.

Part (b)

Now, let's substitute $x = 2$ into the equation $y = 2x + 5$ to find the corresponding $y$-coordinate.

$y = 2(2) + 5 = 4 + 5 = 9$

So, the coordinates of the point of intersection are $(2, 9)$.

Answer:

• For part (a): The coordinates of the point of intersection are $(2, 9)$.
• For part (b): The solution to the simultaneous equations is $x = 2$, $y = 9$.

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:

1. How do you find the point of intersection of two lines algebraically?
2. What happens when two lines are parallel in terms of intersection points?
3. How can you graph simultaneous equations to find their intersection point?
4. How do you interpret the slope and y-intercept in a linear equation like $y = 2x + 5$?
5. Can simultaneous equations always be solved by substitution?

Tip: When solving simultaneous equations graphically, the intersection point represents the solution to the system.