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 (-1.5, 0)
Solution is (-1.5, 0)

Solution is

Answer 1

To solve the given system of equations graphically, we need to plot the two equations on a graph and find their point of intersection.

1. The first equation is: \[ y = -2x - 1 \] This is a linear equation with a slope of -2 and a y-intercept of -1.

2. The second equation can be rearranged to the slope-intercept form (y = mx + b) for easier graphing: \[ 3x - y = -7 \] Rearranging gives: \[ y = 3x + 7 \] This is a linear equation with a slope of 3 and a y-intercept of 7.

Next, we can graph both equations:

• Plot the line for \(y = -2x - 1\). For example:

  • If \(x = 0\), \(y = -1\); point (0, -1)
  • If \(x = -1\), \(y = 1\); point (-1, 1)

• Plot the line for \(y = 3x + 7\). For example:

  • If \(x = 0\), \(y = 7\); point (0, 7)
  • If \(x = -1\), \(y = 4\); point (-1, 4)

After plotting, the intersection point provides the solution for the system of equations.

Using a graphing calculator or software, you would find the point where these two lines intersect.

Upon plotting and analyzing, the intersection occurs at approximately (-1.6, 2.2), which is one of the provided solutions.

So, the solution to the system of equations is:

Solution is (-1.6, 2.2)