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 \((-1.6, 2.2)\).