Question

use the graph to solve the system.
y = -2x + 8
y = x - 2.5

Explanation:

Step1: Recall system solution via graph

The solution to a system of linear equations \( y = -2x + 8 \) and \( y = x - 2.5 \) from a graph is the point of intersection of the two lines.

Step2: Identify intersection point

By looking at the graph, the two lines \( y = -2x + 8 \) and \( y = x - 2.5 \) intersect at a point. From the grid, we can see the \( x \)-coordinate and \( y \)-coordinate of the intersection. Let's check: For \( y=-2x + 8 \) and \( y=x - 2.5 \), the intersection point (from the graph) has \( x = 3.5 \) (or \( \frac{7}{2} \)) and \( y = 1 \) (Wait, no, let's re - check. Wait, let's solve algebraically to confirm. Set \( -2x+8=x - 2.5 \), then \( 8 + 2.5=3x \), \( 10.5 = 3x \), \( x = 3.5 \), then \( y=3.5 - 2.5=1 \)? Wait, no, maybe I misread the graph. Wait, looking at the graph, the intersection seems to be at \( x = 3.5 \) (which is \( \frac{7}{2} \)) and \( y = 1 \)? Wait, no, let's check the grid again. Wait, the \( x \)-axis has labels 1,2,3,4,5,6,7,8. The \( y \)-axis has 1,2,3,4,5. Wait, maybe the intersection is at \( x = 3.5 \) (between 3 and 4) and \( y = 1 \)? Wait, no, let's do the algebra:

Solve \( -2x + 8=x-2.5 \)

Add \( 2x \) to both sides: \( 8=3x - 2.5 \)

Add 2.5 to both sides: \( 10.5 = 3x \)

Divide by 3: \( x = 3.5=\frac{7}{2} \)

Then \( y=x - 2.5=3.5 - 2.5 = 1 \)? Wait, but looking at the graph, the line \( y=x - 2.5 \): when \( x = 3.5 \), \( y = 1 \), and the line \( y=-2x + 8 \): when \( x = 3.5 \), \( y=-2\times3.5 + 8=-7 + 8 = 1 \). So the intersection point is \( (3.5,1) \) or \( (\frac{7}{2},1) \). But maybe the graph's intersection is at \( x = 3.5 \) (7/2) and \( y = 1 \). Wait, but maybe I made a mistake in the graph reading. Alternatively, maybe the intersection is at \( x = 3.5 \) and \( y = 1 \). So the solution to the system is the ordered pair \( (3.5,1) \) or \( (\frac{7}{2},1) \).

Answer:

The solution to the system is \( x = 3.5,y = 1 \) (or \( x=\frac{7}{2},y = 1 \))