Linear Equations(10th Grade > Mathematics ) Questions and answers for exam Preparation

10th Grade > Mathematics

LINEAR EQUATIONS MCQs

Linear Equations In One Variable, Linear Equations In Two Variables, Pair Of Linear Equations In Two Variables (8th, 9th And 10th Grade)

Total Questions : 74 | Page 1 of 8 pages

Question 1. 54 is divided into two parts such that sum of 10 times the first part and 22 times the second part is 780. What is the bigger part?

Discuss Question

Answer: Option A. -> 34
:
A
Let the 2 parts of 54 be x and y
x+y = 54 ....(i)
and 10x + 22y = 780 ...(ii)
Multiply (i) by 10 , we get
10 x + 10 y = 540 ...(iii)
Subtracting (ii) from (iii)
- 12y = - 240
y = 20
Subsituting y = 20 in x + y = 54 ,

⟹

x + 20 = 54

⟹

x = 34
Hence, x = 34 and y = 20

Question 2. The lines that represent these two equations

x + 2 y = 5

and

4 x + 4 y - 6 = 0

meet at only one point (-2, 3.5). The pair of equations is

dependent
consistent
inconsistent
(a) and (b) above.

Discuss Question

Answer: Option B. -> consistent
:
B
A pair of linear equations in two variables which has a solution, is said to beconsistent.
Here the lines representing the given linear equations are meeting only at point (-2, 3.5) giving a unique solution. Therefore, it isa consistent pair of linear equations.
Now, a pair of linear equations in two variables is said to be dependent when the lines representing them are coinciding i.e. will have many solutions.
Here, the lineshave only one solution (-2, 3.5). Therefore, they aren't dependent.

Question 3. For what value of k, the pair of linear equations

3 x + k y = 9

and

6 x + 4 y = 18

has infinitely many solutions?

-5
6
1
2

Discuss Question

Answer: Option D. -> 2
:
D
Given equations gives infinitely many solutions if,

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}

The given linear equations are:

3 x + k y = 9; 6 x + 4 y = 18.

\Rightarrow a_{1} = 3, b_{1} = k, c_{1} = - 9

and

a_{2} = 6, b_{2} = 4, c_{2} = - 18

\Rightarrow \frac{3}{6} = \frac{k}{4} = \frac{- 9}{- 18}

\Rightarrow \frac{1}{2} = \frac{k}{4}

\Rightarrow k = 2

Question 4. Solve the following pair of equations:

2 x + y = 7

3 x + 2 y = 12

Choose the correct answer from the given options.

(2,3)
(3,2)
(1,0)
(-3,2)

Discuss Question

Answer: Option A. -> (2,3)
:
A
We have,

2 x + y = 7

...(1)

3 x + 2 y = 12

...(2)
Multiply equation (1)by 2, we get:

2 (2 x + y) = 2 (7)

\Rightarrow 4 x + 2 y = 14

...(3)
Subtracting (2) from (3) we get ,

x = 2

Substituting the value of

x

in (1) we get,

2 (2) + y = 7 ⟹ y = 3

Thus, the solution for the given pair of linear equations is (2,3).

Question 5. The price of 1 kg oranges is thrice the price of 1 kg apples. Which of the following linear equation represents the given statement ?
(Assume the the price of 1 kg oranges to be x and of 1 kg apples to be y)

x - 3y = 0
2x + 1 = y
x + 3y = 0
3x - y = 0

Discuss Question

Answer: Option A. -> x - 3y = 0
:
A
Given, the price of 1 kg of oranges isx and that of 1 kg of apples isy.
According to the given condition, the price of the 1 kg oranges is three times the price of the 1 kg apple.
So, x = 3y.
Therefore, x - 3y = 0

Question 6. Select the equation whose graph is given alongside:

y = 2x + 2
3y = 6x - 15
y - 2x = 4
y = 2x - 4

Discuss Question

Answer: Option D. -> y = 2x - 4
:
D
By looking at the graph we can easily say that the line passes through the points (2,0) and (0,-4).
We can identify which line passes through these points by substituting the points in the equation of the line.
Plugging x = 2, y = 0 in equation y = 2x - 4, we get
0 = 2(2) - 4 = 0
Plugging x = 0, y = -4 in equation y = 2x - 4, we get
-4 = 2(0) - 0 = -4
Theequation y = 2x - 4 is satisfied by both the points. So, given graph belongs to y = 2x - 4.

Question 7. X = −5 can be expressed as a linear equation in 2 variables.

True
False

Discuss Question

Answer: Option B. -> False
:
B
A linear equation in two variables is of the form ax + by + c = 0, where a and b are both non-zero. If any one of a or b becomes 0, it would reduce to a linear equation in one variable. So, the equation x = -5 cannot be expressed as a linear equation in 2 variables.

Question 8. Why is a first degree polynomial in two variables ax + by + c = 0, called a linear equation?

It has infinitely many solutions
The geometrical representation is a straight line
It has two variables
None of the above

Discuss Question

Answer: Option B. -> The geometrical representation is a straight line
:
B
The degree (the highest power on any variable) of the given equation is 1. Hence, its geometrical representationis a straight line.

Question 9. The points (1,0), (-4,0) and (5,0) lie on

X axis
Y axis
a line parallel to the X axis
a line parallel to the Y axis

Discuss Question

Answer: Option A. -> X axis
:
A
We can observe that all the points have zero as their y coordinates.
(1,0), (-4,0) and (5,0)
y = 0 is the equation of X - axis.
Hence, all the points lie on the X axis.

Question 10. Which of the following equations have