Graph x = 3 and x + y = 1 Step by Step

Step by step

The question

Question: solve by graphing x = 3 and x + y = 1.

① x = 3 and ② x + y = 1

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 ②

On the x-axis, y = 0.

Put 0 in place of y.

x + 0 = 1

Adding 0 changes nothing.

So x = 1.

x = 1

On the y-axis, x = 0.

Put 0 in place of x.

0 + y = 1

0 plus y is just y.

So y = 1.

So line ② crosses the axes at (1, 0) and (0, 1).

y = 1

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.

x = 3: x is always 3.

It is a vertical line: straight up and down.

3 Graph line ②

Put the two crossing points on the grid,

and join them.

4 Where they meet

The lines meet at one point.

Go straight up to the x-axis: x = 3.

Go straight across to the y-axis: y = −2.

So x = 3 and y = −2, both at the same time: the point (3, −2).

(x, y) = (3, −2)

5 Check in both

Let's check: put x = 3 and y = −2 into both equations.

First ①.

x is 3.

It works.

① x = 3

Now ②.

② 3 + (−2) = 3 − 2 = 1

We get 1, the same as the right side.

It works.

(3, −2) is on both lines.

So the answer is right!

Let's look back.

First: crossing points of ②.

Then: graph line ①.

Then: graph line ②.

Then: where they meet.

Last: check in both.

Answer