Question

Solve the system of equations graphically.  You can use your graphing calculator!y=−2x−1 3x − y =−7 (1 point)Responses Solution is (0, 2) Solution is (0, 2) Solution is (-1.6, 2.2 ) Solution is (-1.6, 2.2 ) Solution is (-1, -1) Solution is (-1, -1) Solution is (-1.5, 0)

Answer 1

To solve the system of equations graphically, let's first rewrite both equations in a form that is easier to analyze:

1. The first equation is already in slope-intercept form:
\[
y = -2x - 1
\]

2. The second equation can be rearranged to solve for \(y\):
\[
3x - y = -7 \implies y = 3x + 7
\]

Now, we have the two equations:
- Equation 1: \(y = -2x - 1\)
- Equation 2: \(y = 3x + 7\)

Next, we can find where these two lines intersect. To do this, set the equations equal to each other:
\[
-2x - 1 = 3x + 7
\]
Now, solve for \(x\):
\[
-2x - 3x = 7 + 1
\]
\[
-5x = 8
\]
\[
x = -\frac{8}{5} = -1.6
\]

Substituting \(x = -1.6\) back into either equation to find \(y\). We can use the first equation:
\[
y = -2(-1.6) - 1 = 3.2 - 1 = 2.2
\]

Thus, the solution to the system of equations is approximately:
\[
(-1.6, 2.2)
\]

With this calculation, we see that the correct response is:
**Solution is \((-1.6, 2.2)\)**.