DETERMINE IF THE ORDERED PAIR IS A SOLUTION WORKSHEET

Question 1 :

Check whether (2, -1) is a solution to the following equation.

x + 5y = -3

Question 2 :

Check whether (0, 3) is a solution to the following equation.

7x - y = 4

Question 3 :

Check whether (1, 1) is a solution to the system of equations given below.

2x + 3y = 5

3x - 5y = -2

Question 4 :

Check whether (2, -3) is a solution to the system of equations given below.

x - 2y = 8

2x + y = -1

Question 5 :

Find the value of k, if (2, 1) is a solution to the following equation.

2x +3y = k

Question 6 :

Check which of the following is a  solution to the following equation.

x - 2y = 4

(A) (0, 2)

(B) (2, 0)

(C) (4, 0)

Question 7 :

Is (1, 3) a solution to this system of equations?

x + 4y = 13

5x + 4y = 17

Question 8 :

Given the system

3𝑥 − 2𝑦 = 5

2𝑥 + 3𝑦 = 38

which of the following ordered pairs is a solution?

A) (4, 9) B) (7, 8) C) (11, -3) D) (-5, 10)

Question 9 :

f ℎ(𝑥) =−(1/2) 𝑥 + 3, find h(−27).

A) 33/2     B) 30/3    C)  60     D) (27/2)

Question 10 :

List all the points which are a solution to 2x - y > 4

A) (0, -4)    B) (6, 1)     C) (-2, 4)     D) (1, -2)

1. Answer :

x + 5y = -3

Substitute (2, -1) in the given equation.

2 + 5(-1) = -3 ?

2 - 5 = -3 ?

-3 = -3 ? True

Since the ordered pair (2, -1) makes the given equation true, it is a solution to the equation.

2. Answer :

7x - y = 4

Substitute (0, 3) in the given equation.

7(0) - 3 = 4 ?

0 - 3 = 4 ?

-3 = 4 ? False

Since the ordered pair (0, 3) does not make the given equation true, it is not a solution to the equation.

3. Answer :

2x + 3y = 5

3x - 5y = -2

Substitute (1, 1) in each equation in the given system.

Since the ordered pair (1, 1) makes both equations true, it is a solution to the system.

4. Answer :

x - 2y = 8

2x + y = -1

Substitute (2, -3) in each equation in the given system.

The ordered pair (2, -3) makes only the first equation true and it does not make the second one true

Since, the ordered pair (2, -3) does make both equations true, it is not a solution to the system.

5. Answer :

2x +3y = k

Substitute x = 2 and y = 1.

2(2) + 3(1) = k

7 = k

6. Answer :

(A) (0, 2) :

x - 2y = 4

Substitute x = 0 and y = 2.

0 - 2(2) = 4 ?

-4 = 4 False

Since the ordered pair (0, 2) does not make the given equation true, (0, 2) is not a solution to the equation.

(B) (2, 0) :

x - 2y = 4

Substitute x = 2 and y = 0.

2 - 2(0) = 4 ?

2 - 0 = 4 ?

2 = 4 False

Since the ordered pair (2, 0) does not make the given equation true, (2, 0) is not a solution to the equation.

(C) (4, 0) :

x - 2y = 4

Substitute x = 4 and y = 0.

4 - 2(0) = 4 ?

4 - 0 = 4 ?

4 = 4 True

Since the ordered pair (4, 0) makes the given equation true, (4, 0) is a solution to the equation.

7. Answer :

Substitute (1, 3) in each equation in the given system.

Since the ordered pair (1, 3) makes both equations true, it is a solution to the system.

8. Answer :

3𝑥 − 2𝑦 = 5 -----(1)

2𝑥 + 3𝑦 = 38 -----(2)

Option A :

Applying the point (4, 9) in (1), we get

3(4) - 2(9) = 5

12 - 18 = 5

-6 ≠ 5

So, option A is not the solution for the system of linear equations.

Option B :

Applying the point (7, 8) in (1), we get

3(7) - 2(8) = 5

21 - 16 = 5

5 = 5

Applying in (2), we get

2(7) + 3(8) = 38

14 + 24 = 38

38 = 38

So, (7, 8) is the solution for the system of linear equations.

9. Answer :

ℎ(𝑥) =−(1/2) 𝑥 + 3, find h(−27).

Applying x = -27, we get

= (-1/2)(-27) + 3

= (27/2) + 3

= (27 + 6)/2

= 33/2

So, option A is correct.

10. Answer :

List all the points which are a solution to 2x - y > 4

(6, 1) is the solution 

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