Graphically, the solution is the point or points where the lines or curves intersect. This means to solve a system of equations (linear, quadratic, and so on) by graphing, you follow these steps:

- Graph each function independently but on the same coordinate plane.
- Look for the point or points where the functions intersect.
- Test the points you identified by substituting them into all original equations. While this step is optional, it's highly recommended because graphs can be drawn inaccurately if generated by hand.

## Practice question

- Which system of equations is represented by the following graph?
**A.***y*= 2*x*– 1;*y*=*x*+ 3**B.***y*= –2*x*+ 3;*y*=*x*– 1**C.***y*= –*x*+ 3;*y*= 2*x*– 1**D.***y*= –*x*–1;*y*= 2*x*+ 3

## Answer and explanation

- The correct answer is Choice (B).
The first thing to do is identify the
*y*-intercepts: 3 and –1. Now find the slopes of the lines associated with each of the*y*-intercepts; the line with a*y*-intercept of 3 has a negative slope, which eliminates Choices (A) and (C). Further inspection allows you to conclude that the slope associated with 3 is –2, while the slope of the line with the*y*-intercept of –1 is 1. This means the equation of the two lines is*y*= –2*x*+ 3 and*y*=*x*– 1, which is Choice (B).