Question

solve the following system of equations graphically on the set of axes below.
$y = x - 1$
$y = -dfrac{3}{5}x + 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by solving equations

Set \(x - 1=-\frac{3}{5}x + 7\).
Add \(\frac{3}{5}x\) to both sides: \(x+\frac{3}{5}x-1 = 7\).
Combine like terms: \(\frac{5x + 3x}{5}-1=7\) → \(\frac{8x}{5}-1 = 7\).
Add 1 to both sides: \(\frac{8x}{5}=8\).
Multiply both sides by \(\frac{5}{8}\): \(x = 5\).

Step2: Find y - value

Substitute \(x = 5\) into \(y=x - 1\): \(y=5 - 1=4\).

Answer:

The solution is \((5, 4)\) (the point of intersection of the two lines \(y = x - 1\) and \(y=-\frac{3}{5}x + 7\) when graphed).