Step by step
The question
Question: solve by graphing 2x + y = 2 and x − y = 4.
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.
2x means 2 times x.
We want just x.
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 x is left.
2 divided by 2 is 1.
So x = 1.
On the y-axis, x = 0.
Put 0 in place of x.
2 times 0 is 0.
0 plus y is just y.
So y = 2.
So line ① crosses the axes at (1, 0) and (0, 2).
2 Crossing points of ②
On the x-axis, y = 0.
Put 0 in place of y.
1 times 0 is 0.
Taking away 0 changes nothing.
So x = 4.
On the y-axis, x = 0.
Put 0 in place of x.
0 minus y is −y.
−y means −1 times y.
We want just y.
To remove times −1, we divide by −1.
We do it on both sides, so they stay equal.
−1 divided by −1 is 1.
So just y is left.
Plus over minus is minus.
4 divided by −1 is −4.
So y = −4.
So line ② crosses the axes at (4, 0) and (0, −4).
3 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.
4 Graph line ②
Put the two crossing points on the grid,
and join them.
5 Where they meet
The lines meet at one point.
Go straight up to the x-axis: x = 2.
Go straight across to the y-axis: y = −2.
So x = 2 and y = −2, both at the same time: the point (2, −2).
6 Check in both
Let's check: put x = 2 and y = −2 into both equations.
First ①.
We get 2, the same as the right side.
It works.
Now ②.
We get 4, the same as the right side.
It works.
(2, −2) is on both lines.
So the answer is right!
Let's look back.
First: crossing points of ①.
Then: crossing points of ②.
Then: graph line ①.
Then: graph line ②.
Then: where they meet.
Last: check in both.