The problem asks to solve a system of two linear equations using a given diagram: $y - 2x = 8$ $2x + 5y = 16$ The diagram shows the graphs of these two lines, and the solution to the system is the point where the two lines intersect.

1. Problem Description

The problem asks to solve a system of two linear equations using a given diagram:

$y - 2x = 8$

$2x + 5y = 16$

The diagram shows the graphs of these two lines, and the solution to the system is the point where the two lines intersect.

2. Solution Steps

The solution to the system of equations is the point where the two lines intersect. From the graph, the intersection point appears to be at $(-2, 4)$.

We can verify this by plugging these values into the equations:

For the first equation:

$y - 2x = 4 - 2(-2) = 4 + 4 = 8$. This is correct.

For the second equation:

$2x + 5y = 2(-2) + 5(4) = -4 + 20 = 16$. This is correct.

Therefore, the solution to the simultaneous equations is $x = -2$ and $y = 4$.

3. Final Answer

$x = -2, y = 4$