solving systems of equations by graphing

Answer 1

To solve a system of equations by graphing, follow these steps:

1. Graph each equation on the same coordinate plane.
2. Determine the point(s) where the graphs intersect. These points represent the solution(s) to the system of equations.
3. Check your solution(s) by substituting the coordinate point(s) into the original equations to verify they satisfy both equations.

For example, let's solve the following system of equations by graphing:

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

1. Graph both equations on the same coordinate plane:
- For Equation 1 (y = 2x - 1), plot the y-intercept at -1 and use the slope of 2 to plot additional points to draw a line.
- For Equation 2 (y = -x + 3), plot the y-intercept at 3 and use the slope of -1 to plot additional points to draw a line.

2. Identify the point where the two lines intersect. This point represents the solution to the system of equations.

3. Substitute the coordinates of the point of intersection into both equations to verify that it satisfies both equations.

By following these steps, you can solve systems of equations by graphing.