Step by step
The question
Question: solve by graphing 3x + 2y = 6 and y = x + 3.
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.
2 times 0 is 0.
Adding 0 changes nothing.
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
6 divided by 3 is 2.
So x = 2.
On the y-axis, x = 0.
Put 0 in place of x.
3 times 0 is 0.
0 plus 2y is just 2y.
2y means 2 times y.
We want just y.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just y is left.
6 divided by 2 is 3.
So y = 3.
So line ① crosses the axes at (2, 0) and (0, 3).
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 = 3.
Start on the y-axis at 3.
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 = 0.
It is on the y-axis: y = 3.
So x = 0 and y = 3, both at the same time: the point (0, 3).
5 Check in both
Let's check: put x = 0 and y = 3 into both equations.
First ①.
We get 6, the same as the right side.
It works.
Now ②.
We get 3.
That is y.
It works.
(0, 3) 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.