Pair of Linear Equations in Two Variables Test

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Pair of Linear Equations in Two Variables Test - 60

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Weekly Quiz Competition

Question 1
1 / -0

$$ax+by=c$$ and $$mx+ny=d$$ where $$an\neq bm$$ then these simultaneous equation have -

A
Only one common solution

B
No solution

C
Infinite number of solution

D
Only two solutions.

Solution
Question 2
1 / -0

Giri is 20 year older than his son. If the sum of their ages is 70. how old is his son?

A
5 years

B
20 years

C
25 years

D
30 years

Solution
Question 3
1 / -0

The system of linear equations $$5x+my=10$$ and $$4x+ny=8$$ have infinitely many solutions, where m and n are positive integers. Then the minimum possible value of $$(m+n)$$ is equal to

A
$$9$$

B
$$5$$

C
$$6$$

D
$$10$$

Solution

We know, if two linear equations are $$a_1x+b_1y+c_1=0$$ and $$a_2x+b_2y+c_2=0$$
For infinity many solutions :
$$\Rightarrow$$ $$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$$
Here, the two linear equations are,
$$5x+my=10$$
$$\Rightarrow$$ $$5x+my-10=0$$
$$4x+ny=8$$
$$\Rightarrow$$ $$4x+ny-8=0$$
For, infinity solutions,
$$\Rightarrow$$ $$\dfrac{5}{4}=\dfrac{m}{n}=\dfrac{-10}{-8}$$

$$\Rightarrow$$ $$\dfrac{5}{4}=\dfrac{m}{n}=\dfrac{5}{4}$$

So, the least value of $$m$$ is $$5$$ and $$n$$ is $$4$$.

$$\Rightarrow$$ Minimum possible value of $$(m+n)=5+4=9$$
Question 4
1 / -0

Solve :
$$3x-2y=1$$
$$2x+y=3$$

A
$${1,1}$$

B
$${3,3}$$

C
$${4,4}$$

D
None of thse

Solution

Given:
$$3x-2y=1$$
$$2x+y=3$$

$$y=3-2x$$
$$3x-2(3-2x)=1$$
$$3x-6+4x=1$$
$$7x=7$$
$$x=1$$

$$3(1)-2y=1$$
$$3-2y=1$$
$$2y=2$$
$$y=1$$
Question 5
1 / -0

One equation of a pair of dependent linear equation is $$ -5x +7y = 2 $$ the second equation can be

A
$$ 10x + 14 y + 4 = 0 $$

B
$$ -10 x -14y +4 = 0 $$

C
$$ -10x +14y +4 =0 $$

D
$$ 10x-14y= -4 $$
Question 6
1 / -0

The pair of equations $$ y = 0 $$ and $$ y = -7 $$ has

A
one solution

B
two solution

C
infinitely many solution

D
no solution

Solution

We know that equation of the form $$ y = a $$ is a line parallel to x-axis at distance 'a'from it . $$ y = 0 $$ is the equation of the x-axis and $$ y = -7 $$ is the equation of line parallel to the x-axis so, these two equations two parallel lines . therefore, there is no solution.
hence (D) is correct answers.
Question 7
1 / -0

The system of linear equations $$ x +2y+5=0 $$ and $$ -3x-6y+1=0 $$ have

A
a unique solution

B
exactly two solution

C
infinitely many solutions

D
no solution

Solution

$$ x +2y+5=0 \Rightarrow a_1=1,\,b_1=2,\,c_1=5$$
$$ -3x-6y+1=0 \Rightarrow a_2=-3,\,b_2=-6,\,c_2=1$$
Here,
$$ \dfrac {a_1}{a_2} = \dfrac {1}{-3} = -\dfrac {1}{3} \ ,\ \dfrac {b_1}{b_2} = \dfrac {-1}{3}\ ,\ \dfrac {c_1}{c_2} = \dfrac {5}{1} $$
$$ \therefore \dfrac {a_1}{a_2} = \dfrac {b_1}{b_2} \neq \dfrac {c_1}{c_2} $$
Hence, the system of linear equations has no solution.
Question 8
1 / -0

If $$ x=a, y=b $$ is the solution of the equations $$ x- y=2$$ and $$ x+y=4 $$ then the value of $$ a $$ and $$ b $$ are respectively

A
$$ 3 $$ and $$ 5$$

B
$$ 5 $$ and $$ 3 $$

C
$$ 3 $$ and $$ 1$$

D
$$ -1 $$ and $$ - 3 $$

Solution

If $$ (a.b) $$ is the solution of the given equations, then it mus satisfy the given equations so,
$$ a-b = 2...(i) $$
$$ a+b = 4 .....(ii) $$
$$ \Rightarrow 2a = 6 $$ [ adding (i) and (ii) ]
$$ \Rightarrow a= 3 $$

Now, $$ 3 +b = 4 [ from (ii) ] $$
$$ \Rightarrow b = 1 $$
So, $$ (a,b) = (3,1) $$
Question 9
1 / -0

Choose the correct alternative answers for the following questions.
If $$3x + 5y = 9 $$ and $$5x + 3y= 7$$ then What is the value of $$x + y~ ?$$

A
$$2$$

B
$$16$$

C
$$9$$

D
$$7$$

Solution
Question 10
1 / -0

The solutions of the pair of equations $$ x- y = 0 , x + y = 0 $$

A
$$ x = 3 , y = 5 $$

B
$$ x = 3 , y = 2 $$

C
$$ x = 0 , y = 0 $$

D
$$ x = 5 , y = 5 $$

Solution

Clearly from the graph , the intersection point of $$x-y=0$$ (blue line) and $$x+y=0$$ (brown line) is $$(0,0)$$. Hence, $$x =0 , y=0$$ is the solution of given linear equations.

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Re-Attempt Weekly Quiz Competition

Pair of Linear Equations in Two Variables Test - 60

Result

Pair of Linear Equations in Two Variables Test - 60

Score

-

Rank

-

SHARING IS CARING

Question 1

Only one common solution

No solution

Infinite number of solution

Only two solutions.

Solution

Question 2

5 years

20 years

25 years

30 years

Solution

Question 3

$$9$$

$$5$$

$$6$$

$$10$$

Solution

Question 4

$${1,1}$$

$${3,3}$$

$${4,4}$$

None of thse

Solution

Question 5

$$ 10x + 14 y + 4 = 0 $$

$$ -10 x -14y +4 = 0 $$

$$ -10x +14y +4 =0 $$

$$ 10x-14y= -4 $$

Question 6

one solution

two solution

infinitely many solution

no solution

Solution

Question 7

a unique solution

exactly two solution

infinitely many solutions

no solution

Solution

Question 8

$$ 3 $$ and $$ 5$$

$$ 5 $$ and $$ 3 $$

$$ 3 $$ and $$ 1$$

$$ -1 $$ and $$ - 3 $$

Solution

Question 9

$$2$$

$$16$$

$$9$$

$$7$$

Solution

Question 10

$$ x = 3 , y = 5 $$

$$ x = 3 , y = 2 $$

$$ x = 0 , y = 0 $$

$$ x = 5 , y = 5 $$

Solution

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