The question
Question: solve by graphing y = x + 1 and y = −x + 3.
① y = x + 1 and ② y = −x + 3
The answer is a point that is on both lines.
So we draw both lines and see where they meet.
answer = the point on both lines
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 = 1.
Start on the y-axis at 1.
m = 1.
As a fraction: 1/1.
Go right 1,
then up 1.
Dot.
Join the dots with a straight line.
2 Graph line ②
In ②, b = 3.
Start on the y-axis at 3.
m = −1.
As a fraction: −1/1.
To stay on the grid, we go the other way.
Both moves turn round, so the slope stays the same.
Go left 1,
then up 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 = 1.
Go straight across to the y-axis: y = 2.
So x = 1 and y = 2, both at the same time: the point (1, 2).
(x, y) = (1, 2)
4 Check in both
Let's check: put x = 1 and y = 2 into both equations.
First ①.
① y = 1 + 1 = 2
We get 2.
That is y.
It works.
Now ②.
② y = −1 + 3 = 2
We get 2.
That is y.
It works.
(1, 2) 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.
▶ Watch it solved
The question
Question: solve by graphing y = (1/2)x + 1 and y = −x + 4.
① y = 12x + 1 and ② y = −x + 4
The answer is a point that is on both lines.
So we draw both lines and see where they meet.
answer = the point on both lines
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 = 1.
Start on the y-axis at 1.
m = 1/2.
Go right 2,
then up 1.
Dot.
Join the dots with a straight line.
2 Graph line ②
In ②, b = 4.
Start on the y-axis at 4.
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 = 2.
So x = 2 and y = 2, both at the same time: the point (2, 2).
(x, y) = (2, 2)
4 Check in both
Let's check: put x = 2 and y = 2 into both equations.
First ①.
① y = 12(2) + 1 = 1 + 1 = 2
We get 2.
That is y.
It works.
Now ②.
② y = −2 + 4 = 2
We get 2.
That is y.
It works.
(2, 2) 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.
▶ Watch it solved
The question
Question: solve by graphing 2x + y = 2 and x − y = 4.
① 2x + y = 2 and ② x − y = 4
The answer is a point that is on both lines.
So we draw both lines and see where they meet.
answer = the point on both lines
1 Crossing points of ①
On the x-axis, y = 0.
Put 0 in place of y.
2x + 0 = 2
Adding 0 changes nothing.
2x = 2
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.
2x2 = 22
2 divided by 2 is 1.
So just x is left.
2 divided by 2 is 1.
22 = 1
So x = 1.
x = 1
On the y-axis, x = 0.
Put 0 in place of x.
2 × 0 + y = 2
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).
y = 2
2 Crossing points of ②
On the x-axis, y = 0.
Put 0 in place of y.
x − 1 × 0 = 4
1 times 0 is 0.
Taking away 0 changes nothing.
So x = 4.
x = 4
On the y-axis, x = 0.
Put 0 in place of x.
0 − y = 4
0 minus y is −y.
−y = 4
−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.
−y−1 = 4−1
−1 divided by −1 is 1.
So just y is left.
Plus over minus is minus.
4 divided by −1 is −4.
4−1 = −4
So y = −4.
So line ② crosses the axes at (4, 0) and (0, −4).
y = −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).
(x, y) = (2, −2)
6 Check in both
Let's check: put x = 2 and y = −2 into both equations.
First ①.
① 2(2) + (−2) = 4 − 2 = 2
We get 2, the same as the right side.
It works.
Now ②.
② 2 − (−2) = 2 + 2 = 4
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.
▶ Watch it solved
