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.

Example 8 :

A system of two linear equations has one solution. What must be true about the lines?

A) They are parallel         B) They are perpendicular

C) They are the same line      D) They intersect.

Solution :

The point of intersection of the lines is known as solution. To have solution for the system of equation it must be intersecting lines. If they are intersecting at on point, it should have unique solution, if they are coincident lines (over lapping lines) it may infinite number of solutions. So, option D is correct.

Example 9 :

The functions 𝑓(𝑥) and 𝑔(𝑥) are graphed to the side. Approximate the value 𝑥 when 𝑓(𝑥) = 𝑔(𝑥).

𝑎) 𝑥 = 2.5     𝑏) 𝑥 = −0.9    𝑐) 𝑥 = 3.5     𝑑) 𝑥 = −1

Solution :

By observing the graph clearly,  𝑓(𝑥) = 𝑔(𝑥) at x = 2.5

So, option a is correct.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.