Question

use the graph to solve the system.
y = 2x - 3
y = -3x + 7
graph of two lines: y = 2x - 3 and y = -3x + 7 intersecting
the solution is (\square, \square).

Explanation:

Step1: Recall solution of system

The solution to a system of linear equations graphed is the point of intersection of the two lines.

Step2: Identify intersection point

From the graph, the lines \( y = 2x - 3 \) and \( y=-3x + 7 \) intersect at the point where \( x = 2 \) and \( y=1 \) (by looking at the grid and the intersection coordinates). We can also verify by solving the equations: set \( 2x-3=-3x + 7 \), then \( 2x+3x=7 + 3 \), \( 5x = 10 \), so \( x = 2 \). Substitute \( x = 2 \) into \( y=2x-3 \), we get \( y=2(2)-3=1 \).

Answer:

\( (2, 1) \)