Equations and Their Solutions Quick Check

Identify the value of the variable that is the solution of the equation x – 125 = 375.

• x = 3

• x = 490

• x = 250

• x = 500

Identify the value of the variable that is the solution of the equation 48 = 6w.

• w = 8

• w = 42

• w = 54

• w = 288

Identify the value of the variable that is the solution of the equation k ÷ 7 = 13.

• k = 6

• k = 20

• k = 71

• k = 91

Identify the value of the variable that is the solution of the 9z = 63.

• z = 7

• z = 14

• z = 54

• z = 72

Check which of the following options is not the solution of the equation: 7x – 4y = 16

• (0, - 4)

• (16/7, 0)

• (5, 2)

• (2, -1/2)

Answer explanation

7x – 4y = 16 Taking (x = 5, y = 2) L.H.S = 7(5) - 4(2) = 27 ≠ R.H.S Therefore,(5, 2) is not the solution of the equation 7x – 4y = 16 whereas the remaining options are the solutions of this equation. Therefore option 3 is the correct answer.

Check whether y = -3 is the solution of the equation 2y + 6 = 0

• YES. y = -3 is root

• NO. y = -3 is not a root

Which of the following coordinate points represent solutions for the equation 2x + y = 0?

• 
• 
• 
• 

Answer explanation

The equation is 2x + y = 0 (1) Let's take x = 1 2(1) + y = 0 y = 0 - 2 y = -2 (2) Let's take x = 2 2(2) + y = 0 4 + y = 0 y = -4 (3) Let's take x = 10 2(10) + y = 0 20 + y = 0 y = -20 Hence, option 2 is the correct solution for 2x + y = 0

• Yes

• No

The sum of two numbers is -2.  The difference is -​ 12.  
Find the 2 numbers

​ ​ (a)   ​ (b)   ​

• 5

• -7

• 6

• -4

• 3

• -3

• 2

• -2

Identify the option having two correct solutions for the equation 5x + 4y = 20

• (2,1) and (3,2)

• (1, 4) and (3,1)

• (0, 5) and (4, 0)

• (4, 3) and (3, 0)

Answer explanation

5x + 4y = 20 On taking (x = 0, y = 5), L.H.S = 5(0) + 4(5) = 20 = R.H.S On taking (x = 4, y = 0), L.H.S = 5(4) + 4(0) = 20 = R.H.S Therefore, (0, 5) and (4, 0) are two solutions of the given linear equation in two variables.