Question

Solve the system by graphing:

$\left\{\begin{array}{l}y=-3x-6\\ 6x+2y=-12\end{array}\right.$

Short answer

The system of equations $\left\{\begin{array}{l}y=-3x-6\\ 6x+2y=-12\end{array}\right.$has infinitely many solutions and it can be seen in the graph as,

Step-by-step solution

Step 1. Given Information.

We are given a system of equations $\left\{\begin{array}{l}y=-3x-6\\ 6x+2y=-12\end{array}\right.$and we need to find its solution by graphing.

Step 2. Graph the first equation.

The equation $y=-3x-6$is in slope-intercept form, so its slope is $-3$and its $y$intercept is $-6$.

So, the graph is given as,

Step 3. Graph the second equation on the same rectangular coordinate system.

Solving the equation $6x+2y=-12$for $y$we get,

$\begin{array}{rcl}6x+2y-6x& =& -12-6x\\ 2y& =& -6x-12\\ \frac{2y}{2}& =& \frac{-6x-12}{2}\\ y& =& -3x-6\end{array}$

So the slope of the line is $-3$and its $y$intercept is $-6$. So its graph can be drawn on the same plane as,

Step 4. Identify the solution to the system.

• From the graph, it can be seen that the graph of the equations is the same.
• Since every point on the line makes both equations true, there are infinitely many ordered pairs that make both equations true.
• There are infinitely many solutions to this system.