Question

How do you solve the system by graphing `x – y = 5` and `x + y = 3`?

Answer 1

It would be easiest to convert to slope intercept form to graph,

Explanation:

x - y = 5
-y = 5 - x
y = -5 + x

The slope is + 1 and the y intercept is at -5.

graph{x - y = 5 [-20, 20, -10, 10]}

Sadly, I don't have the software, to present both lines on one graph.

Next, do x + y = 3

x + y = 3
y = 3 - x.

The slope is -1 and the y intercept is 3.

graph{x + y = 3 [-20, 20, -10, 10]}

If they were on the same grid, you would see the intersection point, but since the software doesn't work that way, we'll have to verify algebraically.

x - y = 5
x + y = 3
y = 3 - x
x - (3 - x) = 5
x - 3 + x = 5
2x = 8
x = 4
4 + (y) = 3
y = 3 - 4
y = -1

So, the solution set is (4, -1).

Sorry about the graphing issues. I wish there was a way to show you, but unfortunately I don't know of one on this website.

Hopefully you understand now.