Solve by graphing y = 2x - 1, x + y = 5 Step by Step

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The question

Question: solve by graphing y = 2x − 1 and x + y = 5.

① y = 2x − 1 and ② x + y = 5

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 = 5

Adding 0 changes nothing.

So x = 5.

x = 5

On the y-axis, x = 0.

Put 0 in place of x.

0 + y = 5

0 plus y is just y.

So y = 5.

So line ② crosses the axes at (5, 0) and (0, 5).

y = 5

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.

In ①, b = −1.

Start on the y-axis at −1.

m = 2.

As a fraction: 2/1.

Go right 1,

then up 2.

Dot.

Join the dots with a straight line.

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 down to the x-axis: x = 2.

Go straight across to the y-axis: y = 3.

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

(x, y) = (2, 3)

5 Check in both

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

First ①.

① y = 2(2) − 1 = 4 − 1 = 3

We get 3.

That is y.

It works.

Now ②.

② 2 + 3 = 5

We get 5, the same as the right side.

It works.

(2, 3) 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