Pair of Linear Equations in Two Variables Test

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Pair of Linear Equations in Two Variables Test - 56

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Question 1
1 / -0

The graph of the equations $$x + y = 5$$ and $$x -y = 1$$ will be.....

A
Parallel lines

B
Intersecting lines

C
Lines coincide

D
Concurrent lines

Solution

Take few points on bothe lines and draw the graphs of both lines.

For $$x + y = 5$$:
x 0 3 5
y 5 2 0
For $$x - y = 1$$:
x 0 1 3
y -1 0 2
From the graphs, we can say that the lines are intesecting at $$(3,2)$$.
Question 2
1 / -0

Solve the following pairs of equations.
$$y=2x+1$$; $$y+3x-6=0$$

A
$$\left( 1,3 \right) $$

B
$$\left( 2,3 \right) $$

C
$$\left( 4,3 \right) $$

D
None of these

Solution

Here given equations are $$y-2x= 1$$ ; $$y+3x=6$$
Subtract both the equations, we will get $$x=1$$.
On substituting the value of $$x$$ in any given equations we get $$y=3$$
Question 3
1 / -0

Solve the following pairs of equations.
$$2x-4=0$$; $$4x+y+4=0$$

A
$$\left( 2,-12 \right) $$

B
$$\left( 1,-12 \right) $$

C
$$\left( 2,12 \right) $$

D
None of these

Solution

$$2x-4= 0 \implies x=2$$

and
$$4x+y =-4$$
$$4(2)+y=-4$$
$$8+y =-4$$
$$y =-12$$

$$\Rightarrow x=2, y = -12 $$
Question 4
1 / -0

Solve the following equations by substitution method.
$$\dfrac{1}{x} + \dfrac{2}{y} = 9; \dfrac{2}{x} + \dfrac{1}{y} = 12 (x \neq 0, y \neq 0)$$

A
$$x = \dfrac{1}{5} , y = \dfrac{1}{2}$$

B
$$x = \dfrac{2}{5} , y = \dfrac{1}{2}$$

C
$$x = \dfrac{1}{5} , y = \dfrac{-1}{2}$$

D
None of these

Solution

Given equations,

$$\dfrac{1}{x} + \dfrac{2}{y} = 9$$..............(1)
$$\dfrac{2}{x} + \dfrac{1}{y} = 12$$..............(2)
$$\dfrac{1}{x}=9-\dfrac{2}{y}$$.........from (1)
putting value of $$\dfrac {1}{x}$$ in (2), we get
$$2\left[9-\dfrac{2}{y}\right]+\dfrac{1}{y}=12$$
$$18-\dfrac{3}{y}=12$$
$$6=\dfrac{3}{y}$$......$$\boxed{y=\dfrac{1}{2}}$$
putting value of $$y$$ in (1), we get
$$\dfrac {1}{x}=9-4$$
$$\dfrac{1}{x}=5$$......$$\boxed{x=\dfrac{1}{5}}$$
Question 5
1 / -0

Solve the following equations by substitution method.
$$\dfrac{3}{x} + \dfrac{1}{y} = 7; \dfrac{5}{x} - \dfrac{4}{y} = 6. (x \neq 0, y \neq 0)$$

A
$$x = \dfrac{1}{2}, y = 1$$

B
$$x = \dfrac{-1}{2}, y = 1$$

C
$$x = \dfrac{1}{2}, y = -1$$

D
None of these

Solution

Given equations are,
$$\dfrac{3}{x}+\dfrac{1}{y}=7$$
$$\dfrac{5}{x}-\dfrac{4}{y}=6$$
$$\dfrac{1}{x}=\dfrac{1}{3}\left(7-\dfrac{1}{y}\right)$$.................from (1)
Putting value of $$\dfrac {1}{x}$$ in (1), we get
$$5\left[\dfrac{1}{3}(7-\dfrac{1}{y})\right]-\dfrac{4}{y}=6$$
$$\dfrac{35}{3}-\dfrac{5}{3y}-\dfrac{4}{y}=6$$
$$\dfrac{17}{3}=\dfrac{5+12}{3y}$$
$$\boxed {y=1}$$
Putting value of $$y$$ in (1)
$$\dfrac{1}{x}=\dfrac{1}{3}\times 6\Rightarrow \dfrac {1}{x}=2=\boxed{x=\dfrac{1}{2}}$$
Question 6
1 / -0

Solve following system of equations by elimination method. $$x +2y=7, x-2y=1$$

A
$$\left ( 4, \dfrac{3}{2} \right )$$

B
$$\left ( 4, \dfrac{2}{2} \right )$$

C
$$\left ( 3, \dfrac{3}{2} \right )$$

D
None of these

Solution

Given equations are
$$x+2y=7$$.......(i)

$$x-2y=1$$.........(ii)

Subtract equation (ii) from (i), we get
$$2x=8$$
$$\Rightarrow x=4$$
put value of $$x$$ in equation (ii)
$$4-1=2y$$
$$3=2y$$
$$\therefore y=\dfrac{3}{2}$$
$$\therefore x=4 , \ y=\dfrac{3}{2}$$
Question 7
1 / -0

Solve each of the following system of equations by substitution method.
$$13x +11y=70, 11x+13y=74$$

A
$$(2, 4)$$

B
$$(3, 4)$$

C
$$(2, 2)$$

D
None of these

Solution

Since, $$13x+11y=70$$...eq1 $$11x+13y=74$$......eq2
$$x=\dfrac{70-11y}{13}$$, put this value in eq2, we get
$$11\left[\dfrac{70-11y}{13}\right]+13y=74$$
$$770-121y+169y=74\times 13$$
$$\Rightarrow y=4$$

and
$$x=\dfrac{70-11(4)}{13}$$
$$x=2$$
Question 8
1 / -0

Solve the following equations by substitution method.
$$x + 3y = 10; 2x + y = 5$$

A
$$x = 1, y = 3$$

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

C
$$x = 1, y = 1$$

D
None of these

Solution

$$x+3y=10$$ .....$$(1)$$ ;
$$2x+y=5$$........$$(2)$$

$$y=5-2x$$......from $$(2)$$

putting in $$(1)$$, we get

$$\Rightarrow x+3(5-2x)=10$$

$$\Rightarrow x+15-6x=10$$

$$\Rightarrow -5x=-5$$

$$\Rightarrow x=1$$

$$1+3y=10$$
$$y=3$$
Question 9
1 / -0

Solve the following equations by substitution method.
$$5x + 3y = 21; 2x - y = 4$$

A
$$x = 3, y = 2$$

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

C
$$x = 3, y = -2$$

D
None of these

Solution

$$5x+3y=21$$.........(1)

$$2x-y=4$$...............(2)
$$y=2x-4$$

$$5x+3(2x-4)=21$$.........putting value of $$y$$ in (1)
$$\Rightarrow 5x+6x-12=21$$
$$\Rightarrow 11x=33$$.......................$$\boxed{x=3}$$
Putting value of $$x$$ in (2)
$$6-y=4$$..........................$$\boxed{y=2}$$
Question 10
1 / -0

Solve the following equations by substitution method.
$$2x + y = 1; 3x - 4y = 18$$

A
$$x = 2, y = - 3$$

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

C
$$x = 2, y = 3$$

D
None of these

Solution

$$2x+y=1$$...........(1)

$$3x-4y=18$$........(2)

$$y=1-2x$$...........from (1)

putting value of $$y$$ in (1)

$$\Rightarrow 3x-4(1-2x)=18$$

$$\Rightarrow 3x-4+8x=18$$

$$\Rightarrow 11x=22$$

$$\Rightarrow x=2$$

Using value of $$x$$

$$\Rightarrow 4+y=1$$

$$\Rightarrow y=-3$$

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Re-Attempt Weekly Quiz Competition

Pair of Linear Equations in Two Variables Test - 56

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Pair of Linear Equations in Two Variables Test - 56

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SHARING IS CARING

Question 1

Parallel lines

Intersecting lines

Lines coincide

Concurrent lines

Solution

Question 2

$$\left( 1,3 \right) $$

$$\left( 2,3 \right) $$

$$\left( 4,3 \right) $$

None of these

Solution

Question 3

$$\left( 2,-12 \right) $$

$$\left( 1,-12 \right) $$

$$\left( 2,12 \right) $$

None of these

Solution

Question 4

$$x = \dfrac{1}{5} , y = \dfrac{1}{2}$$

$$x = \dfrac{2}{5} , y = \dfrac{1}{2}$$

$$x = \dfrac{1}{5} , y = \dfrac{-1}{2}$$

None of these

Solution

Question 5

$$x = \dfrac{1}{2}, y = 1$$

$$x = \dfrac{-1}{2}, y = 1$$

$$x = \dfrac{1}{2}, y = -1$$

None of these

Solution

Question 6

$$\left ( 4, \dfrac{3}{2} \right )$$

$$\left ( 4, \dfrac{2}{2} \right )$$

$$\left ( 3, \dfrac{3}{2} \right )$$

None of these

Solution

Question 7

$$(2, 4)$$

$$(3, 4)$$

$$(2, 2)$$

None of these

Solution

Question 8

$$x = 1, y = 3$$

$$x = 2, y = 3$$

$$x = 1, y = 1$$

None of these

Solution

Question 9

$$x = 3, y = 2$$

$$x =- 3, y = 2$$

$$x = 3, y = -2$$

None of these

Solution

Question 10

$$x = 2, y = - 3$$

$$x = -2, y = - 3$$

$$x = 2, y = 3$$

None of these

Solution

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