Question

solve this system of equations by graphing. first graph the equations, and then type the solution.
$y = -\frac{3}{5}x + 2$
$y = -\frac{6}{5}x - 1$
click to select points on the graph.
graph with x-axis from -12 to 10 and y-axis from -10 to 10, with two buttons at the bottom: green for $y = -\frac{3}{5}x + 2$ and orange for $y = -\frac{6}{5}x - 1$

Explanation:

Step1: Find intersection by equating equations

Set \(-\frac{3}{5}x + 2 = -\frac{6}{5}x - 1\)

Step2: Solve for \(x\)

Add \(\frac{6}{5}x\) to both sides: \(\frac{3}{5}x + 2 = -1\)
Subtract 2: \(\frac{3}{5}x = -3\)
Multiply by \(\frac{5}{3}\): \(x = -5\)

Step3: Find \(y\) using \(x = -5\) in \(y = -\frac{3}{5}x + 2\)

\(y = -\frac{3}{5}(-5) + 2 = 3 + 2 = 5\)

Answer:

The solution is \((-5, 5)\)