Step by step
The question
Question: solve by graphing x + y = 4 and y = x − 2.
The answer is a point that is on both lines.
So we draw both lines and see where they meet.
1 Crossing points of ①
On the x-axis, y = 0.
Put 0 in place of y.
Adding 0 changes nothing.
So x = 4.
On the y-axis, x = 0.
Put 0 in place of x.
0 plus y is just y.
So y = 4.
So line ① crosses the axes at (4, 0) and (0, 4).
2 Graph line ①
Draw the grid.
The x-axis goes across.
The y-axis goes up and down.
They meet at 0.
That point is called the origin.
Put the two crossing points on the grid,
and join them.
3 Graph line ②
In ②, b = −2.
Start on the y-axis at −2.
m = 1.
As a fraction: 1/1.
Go right 1,
then up 1.
Dot.
Join the dots with a straight line.
4 Where they meet
The lines meet at one point.
Go straight down to the x-axis: x = 3.
Go straight across to the y-axis: y = 1.
So x = 3 and y = 1, both at the same time: the point (3, 1).
5 Check in both
Let's check: put x = 3 and y = 1 into both equations.
First ①.
We get 4, the same as the right side.
It works.
Now ②.
We get 1.
That is y.
It works.
(3, 1) is on both lines.
So the answer is right!
Let's look back.
First: crossing points of ①.
Then: graph line ①.
Then: graph line ②.
Then: where they meet.
Last: check in both.