Is (2, -1) a solution of 3x - y = 7 and x - 2y = 4

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

Step by step

The question

Question: is (2, −1) a solution of 3x − y = 7 and x − 2y = 4.

① 3x − y = 7 and ② x − 2y = 4

is (2, −1) a solution?

1 Read x and y

The first number is always x.

The second is y.

So x = 2 and y = −1.

(2, −1) → x = 2, y = −1

Careful!

Do not swap them.

The first number in (2, −1) is x.

Careful: not x = −1, y = 2 ✗

2 Check ①

①: Put x = 2 and y = −1 in.

3(2) − (−1) =? 7

Work out each side.

6 + 1 =? 7

Is 7 equal to 7?

Yes.

True!

7 = 7 true

3 Check ②

②: Put x = 2 and y = −1 in.

2 − 2(−1) =? 4

Work out each side.

2 + 2 =? 4

Is 4 equal to 4?

Yes.

True!

4 = 4 true

Both are true.

So (2, −1) is a solution of the system.

(2, −1) is a solution

Let's look back.

First: read x and y.

Then: check ①.

Last: check ②.

Answer

(2, −1) is a solution

Your turn

Try this one yourself, then check:

is (1, −3) a solution of 2x − y = 5 and x − 3y = 10

Show the answer

(1, −3) is a solution