Question

Graph and check to solve the linear system. $$ \begin{aligned} &15 x-10 y=-80\\\ &6 x+8 y=-80 \end{aligned} $$

Short answer

The solution to the system of equations is \((-4,2)\).

Step-by-step solution

Rewrite the Equations In Slope-Intercept Form

First, each equation should be solved for 'y'. Here's how it goes: for the first equation \(15x - 10y = -80\), it can be rewritten as \(y = 1.5x + 8\). Similarly, the second equation \(6x + 8y = -80\) can be rearranged as \(y = -0.75x - 10\).

Graph the Equations

After turning each equation to slope-intercept form, the next step is to graph them. You'll get two lines. One line for each equation.

Find the Intersection

The solution to the system is the coordinates of the point where the two lines intersect. In this case, the lines intersect at point \((-4,2)\).