Question

solve the following system of equations graphically on the set of axes below.
$y = -x + 7$
$y = \frac{3}{2}x - 3$
plot two lines by clicking the graph.
click a line to delete it.
answer attempt 1 out of 2
solution: 1

Explanation:

Step1: Find intersection by solving equations

Set \(-x + 7=\frac{3}{2}x - 3\).
Add \(x\) to both sides: \(7=\frac{3}{2}x+x - 3\).
Combine like terms: \(7=\frac{5}{2}x - 3\).
Add 3 to both sides: \(10=\frac{5}{2}x\).
Multiply both sides by \(\frac{2}{5}\): \(x = 4\).

Step2: Find y - value

Substitute \(x = 4\) into \(y=-x + 7\): \(y=-4 + 7=3\).

Answer:

The solution is \((4, 3)\)