The system of equations is graphed on the coordinate plane.

Question

y=−x−2y=3x+2

Enter the coordinates of the solution to the system of equations in the boxes.

Answer 1

To find the solution to the system of equations given by:

1. $y=-x-2$
2. $y=3x+2$

we can set them equal to each other since they both equal $y$:

$$-x-2=3x+2$$

Now, let's solve for $x$:

1. Add $x$ to both sides: $$-2=4x+2$$

2. Subtract $2$ from both sides: $$-4=4x$$

3. Divide by $4$: $$x=-1$$

Now that we have $x=-1$, we can substitute it back into either equation to find $y$. We'll use the first equation:

$$y=-(-1)-2=1-2=-1$$

Thus, the coordinates of the solution to the system of equations are:

$$(x,y)=(-1,-1)$$

Therefore, the answer is: $$\text{Coordinates: }(-1,-1)$$