Step by step
The question
Question: solve by graphing y = 2x and y = −x + 6.
The answer is a point that is on both lines.
So we draw both lines and see where they meet.
1 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.
In ①, b = 0.
Start on the y-axis at 0.
m = 2.
As a fraction: 2/1.
Go right 1,
then up 2.
Dot.
Join the dots with a straight line.
2 Graph line ②
In ②, b = 6.
Start on the y-axis at 6.
m = −1.
As a fraction: −1/1.
Go right 1,
then down 1.
Dot.
Join the dots with a straight line.
3 Where they meet
The lines meet at one point.
Go straight down to the x-axis: x = 2.
Go straight across to the y-axis: y = 4.
So x = 2 and y = 4, both at the same time: the point (2, 4).
4 Check in both
Let's check: put x = 2 and y = 4 into both equations.
First ①.
We get 4.
That is y.
It works.
Now ②.
We get 4.
That is y.
It works.
(2, 4) is on both lines.
So the answer is right!
Let's look back.
First: graph line ①.
Then: graph line ②.
Then: where they meet.
Last: check in both.