# Question Video: Solving a Linear System of Equations Graphically

Use the graph shown to solve the given simultaneous equations. 𝑦 = −2𝑥 + 3, 𝑦 = 3𝑥 − 2

02:15

### Video Transcript

Use the graph shown to solve the given simultaneous equations. 𝑦 equals negative two 𝑥 plus three and 𝑦 equals three 𝑥 minus two.

When you solve by graphing, all you need to do is look at the graph and decide where they intersect or where the lines cross. So right away, we can actually see that these two lines cross or intersect at the point one, one. From our graph, we had to go right one up one. So 𝑥 is one and 𝑦 is one, so they cross at the point one, one.

While this is our final answer, let’s go ahead and take it a step further and decide which equation goes with which line. Both of our equations are already in slope intercept form, 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚 is your slope and 𝑏 is your 𝑦-intercept. So the slope is the rise over the run. 𝑏, the 𝑦-intercept, is where you crossed the 𝑦-axis.

So for our first equation, 𝑦 equals negative two 𝑥 plus three, we have a negative slope and a 𝑦-intercept of three. So if we have a negative slope, if you look at the line left or right, it should be going down; it’s decreasing. And with a 𝑦-intercept of three, we should cross the 𝑦-axis at three. This would be the blue line.

Our other equation, 𝑦 equals three 𝑥 minus two, three is our slope. So it’s positive. So our graph should be going up left or right or increasing. And the 𝑦-intercept is negative two, so we should be crossing the 𝑦-axis at negative two which does go with the other line, the red line. So overall, we use the graph shown to solve the given simultaneous equations by seeing where they intersected, and that was at the point one, one.