Question

Solve the following system of equations graphically on the set of axes below.

Answer 1

Answer: The solution is (2, 2)

Step-by-step explanation:

We have the system of equations:

y = 2*x - 2

x + y = 4

The first step is to write both equations as linear equations in the slope-intercept form.

y = 2*x - 2

y = -x + 4

Now we have two lines, and we can just graph them, the easiest way is the replace the value of x and obtain two points that belong to the line, and then draw a line that passes through both lines.

For example with the first one, we can firt replace x by 0 to get:

y = 2*0 - 2

y = -2

Then the point (0, -2) belongs to this line.

Now we can replace x by 1 to get:

y = 2*1 - 2 = 0

y = 0

The point (1, 0) belongs to this line.

Then we can draw these two points in the graph, and just draw a line that passes through these two points.

Once you have your two lines drawn, the solution of the system will be the point in which the lines intersect.

Below, you can see the two lines graphed (the green is the first one and the red is the second one)

And we can see that they intersect in the point (2, 2)

Then the solution of the system is (2, 2)