Graph the system of equations

Q:  Graph the system of linear equations, determine the number of solutions, and find the solution:

y = 4x + 2 and y =- 2x – 3

A: Okay, for the sake of talking about the lines I will name them:

Line 1:  y = 4x + 2

Line 2:  y =- 2x – 3

A “solution” to a system of linear equations is the point where the lines intersect.  So, we need to graph both of these lines on the same grid and see if and where they intersect.

Step 1:  Graph Line 1 and Line 2 on the same grid:

Tricks for graphing line 1:  Since line 1 is in the form y = mx + b, we can use the method of finding the slope and the y-intercept to graph the line.

The slope of line 1 is 4 and the y-intercept of line 1 is 2.

On your x-y graph, go up 2 on the y-axis and put a point [this is the y-intercept, or the “b” value]

Now, starting from the y-intercept point 2:  go up 4 and right 1 (this is the slope 4/1).  Create another point.  Connect the dots to make a line.  You should have:


Now, we need the same strategy to graph line 2 on the same grid.

Line 2:  y =- 2x – 3

The y-intercept is -3 and the slope is -2.  Plot the y-intercept of -3 on the y-axis.  From that point:  go down 2, right 1 to create another point.  Connect the dots to make a line.  Your graph should now look like:

So, the question now is:  How many solutions are there and what is the solution.  Recall, the solution is (x, y) point of intersection.
Clearly, there is 1 solution.  The lines do cross at 1 point.

What is that point?  Well, you have to estimate that point from the graph.  This is one problem with solving a system by graphing — it can be inaccurate.  Depending on the “neatness” of your graph, your answer will vary.

To me, the answer appears to be around the point (-.8, -1.3)

*To get the accurate solution, we solve these types of problems algebraically.

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