Question

Which graph can be used to find the solution to the system of equations below?

$$\begin{gathered} 2x+y=-4 \\ -3y=2x+12 \end{gathered}$$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

The explanation for the correct option:

Given system of equations are

$2x+y=-4...\left(1\right)$

and

$$\begin{gathered} -3y=2x+12 \\ \Rightarrow 2x+3y=-12...\left(2\right) \end{gathered}$$

Subtract $\left(1\right)$ from $\left(2\right)$ as follow:

$$\begin{gathered} 2x+3y-\left(2x+y\right)=-12-\left(-4\right) \\ \Rightarrow 3y-y=-12+4 \\ \Rightarrow 2y=-8 \\ \therefore y=-4 \end{gathered}$$

.Put $y=-4$in the equation $\left(1\right)$

$$\begin{gathered} 2x-4=-4 \\ \Rightarrow 2x=-4+4 \\ \Rightarrow 2x=0 \\ \therefore x=0 \end{gathered}$$

Thus the intersection point is $\left(0,-4\right)$.

In the graph of option $\mathrm{A}$ , the lines intersects at point $\left(0,-4\right)$.

The explanation for the incorrect options.

Since the intersection point of the given line is. And the lines in other graphs do not intersect at $\left(0,-4\right)$.

So, the options B, C, and D are incorrect.

Hence, the correct option is $\left(\mathrm{A}\right)$.