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Checking a solution

Algebra 1 ยท 25 problems, easy to harder

โ–ถ Watch the first one solved

How we do it

  1. Read x and y
  2. Put them in

The steps for Is (2, 1) a solution of 3x + y = 7. Every solution names its steps, so you always know what comes next.

Worked examples

Is (2, 1) a solution of 3x + y = 7 Easy

The question

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

3x + y = 7
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) โ†’ x = 2, y = 1

Careful!

Do not swap them.

The first number in (2, 1) is x.

Careful: not x = 1, y = 2 โœ—

2 Put them in

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

It is true.

So (2, 1) is a solution.

(2, 1) is a solution

Let's look back.

First: read x and y.

Last: put them in.

Answer
(2, 1) is a solution

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

The question

Question: is (โˆ’2, 3) a solution of y = โˆ’x + 1.

y = โˆ’x + 1
is (โˆ’2, 3) a solution?

1 Read x and y

The first number is always x.

The second is y.

So x = โˆ’2 and y = 3.

(โˆ’2, 3) โ†’ x = โˆ’2, y = 3

Careful!

Do not swap them.

The first number in (โˆ’2, 3) is x.

Careful: not x = 3, y = โˆ’2 โœ—

2 Put them in

Put x = โˆ’2 and y = 3 in.

3 =? โˆ’(โˆ’2) + 1

Work out each side.

3 =? 2 + 1

Is 3 equal to 3?

Yes.

True!

3 = 3 true

It is true.

So (โˆ’2, 3) is a solution.

(โˆ’2, 3) is a solution

Let's look back.

First: read x and y.

Last: put them in.

Answer
(โˆ’2, 3) is a solution

โ–ถ Watch it solved

Is (1, 2) a solution of y > 2x - 1 Harder

The question

Question: is (1, 2) a solution of y > 2x โˆ’ 1.

y > 2x โˆ’ 1
is (1, 2) a solution?

1 Read x and y

The first number is always x.

The second is y.

So x = 1 and y = 2.

(1, 2) โ†’ x = 1, y = 2

Careful!

Do not swap them.

The first number in (1, 2) is x.

Careful: not x = 2, y = 1 โœ—

2 Put them in

Put x = 1 and y = 2 in.

2 >? 2(1) โˆ’ 1

Work out each side.

2 >? 2 โˆ’ 1

Is 2 more than 1?

Yes.

True!

2 > 1 true

It is true.

So (1, 2) is a solution.

(1, 2) is a solution

Let's look back.

First: read x and y.

Last: put them in.

Answer
(1, 2) is a solution

โ–ถ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. is (2, 1) a solution of 3x + y = 7
    Answer
    (2, 1) is a solution
  2. is (1, 4) a solution of 2x + y = 5
    Answer
    (1, 4) is not a solution
  3. is (3, 2) a solution of x + y = 5
    Answer
    (3, 2) is a solution
  4. is (2, 3) a solution of x + 2y = 7
    Answer
    (2, 3) is not a solution
  5. is (4, 1) a solution of 2x - y = 7
    Answer
    (4, 1) is a solution
  6. is (0, 3) a solution of 4x + y = 3
    Answer
    (0, 3) is a solution
  7. is (5, 2) a solution of x - 3y = 1
    Answer
    (5, 2) is not a solution
  8. is (1, 1) a solution of 5x - 2y = 3
    Answer
    (1, 1) is a solution
  9. is (2, 5) a solution of y = 2x + 1
    Answer
    (2, 5) is a solution
  10. is (3, 4) a solution of y = 3x - 4
    Answer
    (3, 4) is not a solution

Medium

  1. is (-2, 3) a solution of y = -x + 1
    Answer
    (โˆ’2, 3) is a solution
  2. is (4, -1) a solution of y = 1/2x - 3
    Answer
    (4, โˆ’1) is a solution
  3. is (-1, -3) a solution of 2x - y = 1
    Answer
    (โˆ’1, โˆ’3) is a solution
  4. is (3, -1) a solution of y = -x + 2
    Answer
    (3, โˆ’1) is a solution
  5. is (-4, 2) a solution of x + 3y = 2
    Answer
    (โˆ’4, 2) is a solution
  6. is (2, -1) a solution of 3x - y = 7 and x - 2y = 4
    Answer
    (2, โˆ’1) is a solution
  7. is (3, 2) a solution of 3x - y = 7 and x - 2y = 4
    Answer
    (3, 2) is not a solution
  8. is (1, 3) a solution of x + y = 4 and 2x - y = -1
    Answer
    (1, 3) is a solution
  9. is (-2, 4) a solution of y = -x + 2 and x + 2y = 6
    Answer
    (โˆ’2, 4) is a solution
  10. is (0, -2) a solution of y = 3x - 2 and x + y = 1
    Answer
    (0, โˆ’2) is not a solution

Harder

  1. is (1, 2) a solution of y > 2x - 1
    Answer
    (1, 2) is a solution
  2. is (3, 1) a solution of y < x - 1
    Answer
    (3, 1) is a solution
  3. is (2, 1) a solution of y > x + 1 and x + y < 5
    Answer
    (2, 1) is not a solution
  4. is (1, -1) a solution of x - y >= 2 and y < 2x + 1
    Answer
    (1, โˆ’1) is a solution
  5. is (-1, 3) a solution of 2x + y <= 1 and y >= x + 4
    Answer
    (โˆ’1, 3) is a solution