DETERMINE IF THE ORDERED PAIR IS A SOLUTION

Example 1 :

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

x + 5y = -3

Solution :

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.

Example 2 :

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

7x - y = 4

Solution :

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.

Example 3 :

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

2x + 3y = 5

3x - 5y = -2

Solution :

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.

Example 4 :

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

x - 2y = 8

2x + y = -1

Solution :

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.

Example 5 :

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

2x +3y = k

Solution :

2x +3y = k

Substitute x = 2 and y = 1.

2(2) + 3(1) = k

7 = k

Example 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)

Solution :

(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.

Example 7 :

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

x + 4y = 13

5x + 4y = 17

Solution :

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.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.