Without constructing, find the coordinates of the intersection points, x + y = 10, and the straight line 2y-x = 5.

1. Express one variable from another. In this case, “x”.

For the first graph:

x + y = 10;

x = 10 – y.

For the second graph:

2y – x = 5;

-x = 5 – 2y;

x = -5 + 2y.

Equate the two graphs and find “y”

10 – y = -5 + 2y;

-3y = -15;

y = 5.

Now we substitute the value “y” in the first or second graph and find “x”

If “y” is 5, then

x = 10 – y;

x = 10 – 5 = 5.

This means that the intersection of the two graphs will be at the point (5; 5).