# Linear Equation Questions For SSC GD PDF

LINEAR EQUATION QUESTIONS FOR SSC GD PDF

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**Question 1:Â **A linear equation has 4 variables. What is the least number of equations do you need to figure out the values of all 4 variables?

a)Â 2

b)Â 3

c)Â 4

d)Â 5

e)Â 8

**Question 2:Â **Solve the following system of linear equations and determine the value of x + y + z.

3x + 2y + z = 25

5x + 3y + z = 40

x + 4y + 2z = 10

a)Â 20

b)Â 10

c)Â 5

d)Â 15

e)Â Cannot be determined

**Question 3:Â **At least how many equations are required to determine the values of all the variables in a linear equation with 3 variables

a)Â 1

b)Â 2

c)Â 3

d)Â 4

e)Â 5

**Question 4:Â **How many solutions do the following set of equations have?

$2x+3y=9$ and $4x+6y=18$

a)Â Unique solution

b)Â No solution

c)Â Infinite solutions

d)Â Cannot be determined

e)Â None of these

**Question 5:Â **How many solutions do the following set of equations have?

$2x+3y=9$ and $4x+6y=27$

a)Â Unique solution

b)Â No solution

c)Â Infinite solutions

d)Â Cannot be determined

e)Â None of these

**Question 6:Â **How many solutions do the following set of equations have?

$2x+3y=9$ and $3x+2y=9$

a)Â Unique solution

b)Â No solution

c)Â Infinite solutions

d)Â Cannot be determined

e)Â None of these

**Question 7:Â **The number obtained by interchanging the digits of a two-digit number is less than the original number by 63 If the sum of the digits of the number is 11, what is the original number ?

a)Â 29

b)Â 92

c)Â 74

d)Â Cannot be determined

e)Â None of these

**Question 8:Â **Two linear equations 3x+5y=20, 24x+40y=K will have no solution for x and y when k = ?

a)Â 160

b)Â 8

c)Â 40

d)Â both b and c

**Question 9:Â **x+3y=12 and 5x+15y=3k are two linear equations then for what value of k will the equations have infinite solutions ?

a)Â 0

b)Â 4

c)Â 20

d)Â 12

**Question 10:Â **How many solutions does a pair of linear equations will have, if the equations are

7x+4y-16=0 and 14x+6y-32=0?

a)Â 0

b)Â 1

c)Â 2

d)Â Infinite

**Answers & Solutions:**

**1)Â AnswerÂ (C)**

To uniquely determine each of the given variable, we need the number of equations to be at least equal to the number of variables. Hence for 4 variables, we need at least 4 equations to uniquely determine the value of each variable.

**2)Â AnswerÂ (D)**

3x + 2y + z = 25 (I)

5x + 3y + z = 40 (II)

x + 4y + 2z = 10 (III)

II – I gives

2x + y = 15 (IV)

2*(I) – III gives

5x = 40

=> x = 8

Putting value of x in equation IV gives

y = -1

Putting value of x and y in I gives z = 3

So required sum is 8+3-1 = 10

**3)Â AnswerÂ (C)**

In a linear equation with 3 variables, we will have 3 unknowns and so we will need at least 3 equations to uniquely determine the value of all three variables.

**4)Â AnswerÂ (C)**

The two linear equations, $ a_{1}x+b_{1}y=c1$ and $ a_{2}x+b_{2}y=c2$ :

Have a unique solution if $\frac{a_{1}}{a_{2}}\neq\frac{b_{1}}{b_{2}}$

Have no solution if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$

Have infinite solutions if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

In the given equations $\frac{2}{4}=\frac{3}{6}=\frac{9}{18}$. So the equations have infinite solutions.

**5)Â AnswerÂ (B)**

The two linear equations, $ a_{1}x+b_{1}y=c1$ and $ a_{2}x+b_{2}y=c2$ :

Have a unique solution if $\frac{a_{1}}{a_{2}}\neq\frac{b_{1}}{b_{2}}$

Have no solution if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$

Have infinite solutions if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

In the given equations $\frac{2}{4}=\frac{3}{6}\neq\frac{9}{27}$. So the equations have no solution.

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**6)Â AnswerÂ (A)**

The two linear equations, $ a_{1}x+b_{1}y=c1$ and $ a_{2}x+b_{2}y=c2$ :

Have a unique solution if $\frac{a_{1}}{a_{2}}\neq\frac{b_{1}}{b_{2}}$

Have no solution if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$

Have infinite solutions if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

In the given equations $\frac{2}{3}\neq\frac{3}{2}$. So the equations have a unique solution.

**7)Â AnswerÂ (B)**

Let units place digit be x and tens place digit be y.

Original number = 10y + x

Number obtained on interchanging the digits = 10x +y

By given conditond,

x+y = 11

10x +y = 10y +x – 63

9y – 9x = 63

y – x = 7

Solving the linear equations we get,

y=9 and x=2

Original number is 92 i.e option B.

**8)Â AnswerÂ (D)**

For the given two equations 3x+5y=20 and 24x+40y=k

8(3x+5y)=k

3x+5y=($\frac{k}{8}$)

They have infinite solutions if k=160 and for all other values of k it will have no solution.

**9)Â AnswerÂ (C)**

x+3y=12$\rightarrow$ 1

5(x+3y)=3k

x+3y=$\frac{3k}{5}\rightarrow$ 2

These both equations represent a single equation and have infinite solutions when $\frac{3k}{5}$=12.

$\therefore$ k=20.

**10)Â AnswerÂ (B)**

Equations : 7x+4y-16=0 and 14x+6y-32=0

Comparing the ratio of coefficients of both equations,

=> $\frac{7}{14}\neq\frac{4}{6}$

Thus, there is only 1 solution.

=> Ans – (B)