Solve the system of equations graphically. You can use your graphing calculator!

Question

y=−2x−1

3x − y =−7

(1 point)
Responses

Solution is (-1.6, 2.2 )
Solution is (-1.6, 2.2 )

Solution is (-1, -1)
Solution is (-1, -1)

Solution is (0, 2)
Solution is (0, 2)

Solution is (-1.5, 0)

Answer 1

To solve the system of equations graphically, we will analyze the two equations provided:

1. \( y = -2x - 1 \)
2. \( 3x - y = -7 \)

First, we will rewrite the second equation in slope-intercept form (y = mx + b):

Starting with \( 3x - y = -7 \): \[ -y = -3x - 7 \] Multiply by -1: \[ y = 3x + 7 \]

Now we have two equations to graph:

1. \( y = -2x - 1 \) (which has a slope of -2 and y-intercept of -1)
2. \( y = 3x + 7 \) (which has a slope of 3 and y-intercept of 7)

Graph both equations:

• The first equation, \( y = -2x - 1 \), can be plotted by starting at the y-intercept (0, -1) and using the slope to find another point. With a slope of -2, you go down 2 units and right 1 unit to plot another point.

• The second equation, \( y = 3x + 7 \), starts at the y-intercept (0, 7) and from there, using the slope of 3, go up 3 units and right 1 unit to plot additional points.

Find the intersection point:

Once both lines are graphed, the intersection point (if it exists) represents the solution of the system of equations.

From analyzing the graphs, if we perform an intersection check or look closely, we see that the intersection occurs at approximately \( (-1.6, 2.2) \).

Based on the choices provided:

• The nearest solution you have listed is Solution is (-1.6, 2.2).

Therefore, the solution to the system of equations is: Solution is (-1.6, 2.2).