SOLUTION: On a graph paper, draw the two straight lines which represent the equations 2x – y = 3 and 3x + 2y = 1. Also, find their point of intersection of the two lines on the graph paper.

Hi, there--

THE PROBLEM:
On a graph paper, draw the two straight lines which represent the equations 2x – y = 3 and
3x + 2y = 1. Also, find their point of intersection of the two lines on the graph paper.


A SOLUTION:

I like to rewrite the equations in slope-intercept form because it makes them easy to graph.
Start with the first equation:
2x - y = 3

Subtract 2x from both sides.
-y = -2x = 3

Multiply both sides by -1.
y = 2x - 3

Now, the second equation:
3x + 2y = 1

Subtract 3x from both sides.
2y = -3x + 1

Divide both sides by 2.
y = (-3/2)x + (1/2)

Here is a graph of the two lines:
The first line (red) has a slope of 2, and a y-intercept at (0,-3).
The second line (green) has a slope of -3/2 and a y-intercept of 1/2.




It appears that the lines intersect near (1,-1).

We can verify that with algebra:

Substitute 1 for x and -1 for y in both equations:
2x – y = 3 -----> 2(1) - (-1) = 3 -----> 2 + 1 = 3 TRUE!

3x + 2y = 1 ---> 3(1) + 2(-1) = 1 ----> 3 - 2 = 1 TRUE!

Yes, (1,-1) is the intersection point of the two lines.


Hope this helps! Feel free to email if you have any questions.

Mrs. Figgy
math.in.the.vortex@gmail.com