Solve the system of equations by graphing.

Question

How many solutions?

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

Answer 1

To solve the system of equations by graphing, we'll first rewrite both equations in slope-intercept form (y = mx + b) and then plot them.

1. The first equation is already in slope-intercept form: \[ y = -2x + 3 \] This has a slope (m) of -2 and a y-intercept (b) of 3.

2. For the second equation, we'll rearrange it to solve for y: \[ -2x = y + 1 \ y = -2x - 1 \] This equation also has a slope of -2 but a different y-intercept of -1.

Now we can graph both equations:

• For \(y = -2x + 3\):

  • If \(x = 0\), then \(y = 3\) (point: (0, 3))
  • If \(x = 1\), then \(y = 1\) (point: (1, 1))

• For \(y = -2x - 1\):

  • If \(x = 0\), then \(y = -1\) (point: (0, -1))
  • If \(x = 1\), then \(y = -3\) (point: (1, -3))

When we plot these points, we see that both lines have the same slope (-2), which means they are parallel. Since parallel lines never intersect, there are no solutions to this system of equations.

Conclusion: The system of equations has no solutions.