Equations in One Variable Test

Result

Equations in One Variable Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

If the value of y is 1 in 3x + y = 10, then what is the value of x?

A
3

B
4

C
5

D
6

Solution

3x + y = 10
3x + 1 = 10
3x = 10 – 1
3x = 9
x =
x = 3
Question 2
1 / -0

Find the value of a in .

A

B

C

D
1

Solution
Question 3
1 / -0

If the sum of two consecutive numbers is 17, then find the numbers.

A
3, 4

B
6, 7

C
8, 9

D
7, 10

Solution

Let the missing numbers be n and n + 1.
n + (n + 1) = 17
2n + 1 = 17
2n = 17 – 1
2n = 16
n =
n = 8
So, first number is 8.
Second number = n + 1 = 9
Question 4
1 / -0

Assume that the age of a boy is x and the age of a girl is 2x. If we add their ages, then the sum of their ages is 15 years.What would be the age of the boy and the girl?

A
6 years, 9 years

B
5 years, 10 years

C
3 years, 12 years

D
1 year, 14 years

Solution

x + 2x = 15
3x = 15
x =
x = 5
Boy's age = 5 years
Girl's age = 2x = 10 years
Question 5
1 / -0

If the sum of five consecutive multiples of 6 is 390, find the largest multiple.

A
300

B
90

C
78

D
66

Solution

Let the multiples be 6x, 6x + 6, 6x + 12, 6x + 18 and 6x + 24.
A.T.Q.
6x + 6x + 6 + 6x + 12 + 6x + 18 + 6x + 24 = 390
30x + 60 = 390
30x = 390 - 60
30x = 330
x = 11
Largest multiple = 6x + 24 = 6x 11 + 24
= 66 + 24 = 90
Question 6
1 / -0

Solve for a: 2a + 8 = 14

A
3

B
5

C
8

D
10

Solution

2a + 8 = 14
2a = 14 – 8
a = 3
Question 7
1 / -0

If y = 2 for y = 3x - 6, then x is

A
a fraction

B
an integer

C
a negative rational number

D
a whole number

Solution

y = 3x - 6
2 + 6 = 3x
8 = 3x
8/3 = x
x = 8/3, which is a fraction.
Question 8
1 / -0

Find the value of x for which the expressions 6x - 2 and 2x - 2 become equal.

A
0

B
3

C
5

D
6

Solution

6x - 2 = 2x - 2
4x = 0
x = 0
Hence, for x = 0, the expressions will be equal.
Question 9
1 / -0

How many maximum number of solutions does a linear equation in two variables have?

A
Infinity

B
Zero

C
Three

D
Two

Solution

Consider an equation 6x + 2y = 0
You can have infinite number of solutions by trying different combinations of x and y.
Thus, a linear equation in two variables has infinite number of solutions.
Question 10
1 / -0

Which of the following is not a linear equation?

A
6x + 4 = 0

B
4y + 3 = 0

C
3x = 0

D
4x = 4x

Solution

A linear equation has some variables which are denoted by some letter. So, option 4 is not a linear equation.
Question 11
1 / -0

How many solutions will a linear equation in one variable 2x = 5 have?

A
0

B
1

C
2

D
3

Solution

A linear equation in one variable can have only one solution.
Question 12
1 / -0

Solve:

A
Z = 3

B
Z = 5

C
Z = 12

D
Z = 60

Solution

9Z = 4(Z + 15) (by cross multiplication)
5Z = 60
Z = 12
Question 13
1 / -0

What is the solution of the equation 15(y - 4) - 2(y - 9) + 5(y + 6) = 0?

A

B

C

D

Solution

15(y - 4) - 2(y - 9) + 5(y + 6) = 0
15y - 60 - 2y + 18 + 5y + 30 = 0
18y - 60 + 48 = 0
18y - 12 = 0
18y = 12
y =
Question 14
1 / -0

What is the solution of the equation ?

A
n = 21

B
n = 24

C
n = 36

D
n = 48

Solution

n = 3 x 12
n = 36
Question 15
1 / -0

What is the solution of the equation ?

A
x = 3

B
x = 5

C
x = 8

D
x = 16

Solution

5(x - 5) = 3(x - 3) (By cross-multiplication)
5x - 25 = 3x - 9
5x - 3x = -9 + 25
2x = 16
x = (16/2)
x = 8