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We want to determine how many solutions the system ${y=2x+3y=2x−5 $ has by graphing the equations. First step is to draw the graphs on the same set of axes.

In the graph we can see that the lines have different $y$-intercepts and it looks like they are parallel. The equations tell us that the lines have the same slope, $m=2,$ and that means that they are parallel. Parallel lines with different $y$-intercept never intersect. Therefore, the system has **no solution**.

b

Here we want to find out how many solutions the following system has. ${y=-3x+8y=3x−4 $ First we are going to graph the equations. After that we will determine the number of solutions by looking for point(s) of intersection between the lines.

In the graph we can see that the lines have one point of intersection. Therefore, the system has **one solution**.