Question

What is the solution of the system y=-5x-2 y+2=-5x

Answer 1

`\left\{\begin{array}{ccc}y=-5x-2\\y+2=-5x&\text{subtract 2 from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}y=-5x-2\\y=-5x-2&\text{multiply both sides by (-1)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}y=-5x-2\\-y=5x+2\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad0=0\qquad TRUE\\\\Answer:\ \text{The system has infinite solutions}\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\y=-5x-2\end{array}\right`

Answer 2

Infinite

Explanation:

y=-5x-2

y+2=-5x

Rearrange the second equation

y=-5x-2

Since the equations are the same, there are infinite solutions