Question

solve this system of equations by graphing. first graph the equations, and then type the solution.
$y = \frac{3}{5}x + 7$
$y = \frac{1}{5}x + 5$
click to select points on the graph.
graph with grid, axes from -10 to 10, and two equation buttons: $y = \frac{3}{5}x + 7$ (purple) and $y = \frac{1}{5}x + 5$ (blue)
the solution is...

Explanation:

Step1: Set equations equal

Since \( y = \frac{3}{5}x + 7 \) and \( y = \frac{1}{5}x + 5 \), set \( \frac{3}{5}x + 7=\frac{1}{5}x + 5 \).

Step2: Solve for x

Subtract \( \frac{1}{5}x \) and 7 from both sides: \( \frac{3}{5}x-\frac{1}{5}x=5 - 7 \). Simplify: \( \frac{2}{5}x=-2 \). Multiply both sides by \( \frac{5}{2} \): \( x=-2\times\frac{5}{2}=-5 \).

Step3: Find y

Substitute \( x = - 5 \) into \( y=\frac{1}{5}x + 5 \): \( y=\frac{1}{5}(-5)+5=-1 + 5 = 4 \).

Answer:

\((-5, 4)\)