Is (1, 3) a solution of x + y = 4 and 2x - y = -1

Step by step, with the reason for every step · Checking a solution · Algebra 1

Step by step

The question

Question: is (1, 3) a solution of x + y = 4 and 2x − y = −1.

① x + y = 4 and ② 2x − y = −1

is (1, 3) a solution?

1 Read x and y

The first number is always x.

The second is y.

So x = 1 and y = 3.

(1, 3) → x = 1, y = 3

Careful!

Do not swap them.

The first number in (1, 3) is x.

Careful: not x = 3, y = 1 ✗

2 Check ①

①: Put x = 1 and y = 3 in.

1 + 3 =? 4

Work out each side.

Is 4 equal to 4?

Yes.

True!

4 = 4 true

3 Check ②

②: Put x = 1 and y = 3 in.

2(1) − 3 =? −1

Work out each side.

2 − 3 =? −1

Is −1 equal to −1?

Yes.

True!

−1 = −1 true

Both are true.

So (1, 3) is a solution of the system.

(1, 3) is a solution

Let's look back.

First: read x and y.

Then: check ①.

Last: check ②.

Answer

(1, 3) is a solution

Your turn

Try this one yourself, then check:

is (2, 2) a solution of x + y = 4 and 5x − y = 8

Show the answer

(2, 2) is a solution