Is (1, -1) a solution of x - y >= 2 and y < 2x + 1

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

Step by step

The question

Question: is (1, −1) a solution of x − y ≥ 2 and y < 2x + 1.

① x − y ≥ 2 and ② y < 2x + 1

is (1, −1) a solution?

1 Read x and y

The first number is always x.

The second is y.

So x = 1 and y = −1.

(1, −1) → x = 1, y = −1

Careful!

Do not swap them.

The first number in (1, −1) is x.

Careful: not x = −1, y = 1 ✗

2 Check ①

①: Put x = 1 and y = −1 in.

1 − (−1) ≥? 2

Work out each side.

1 + 1 ≥? 2

Is 2 more than or equal to 2?

Yes.

True!

2 ≥ 2 true

3 Check ②

②: Put x = 1 and y = −1 in.

(−1) <? 2(1) + 1

Work out each side.

−1 <? 2 + 1

Is −1 less than 3?

Yes.

True!

−1 < 3 true

Both are true.

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

(1, −1) is a solution

Let's look back.

First: read x and y.

Then: check ①.

Last: check ②.

Answer

(1, −1) is a solution

Your turn

Try this one yourself, then check:

is (5, −5) a solution of x − y ≥ 10 and y < 2x − 11

Show the answer

(5, −5) is a solution