Pair of Linear Equations in Two Variables Test

Directions For Questions

If we have two simultaneous equations
$$ax+by=c$$ -------(1)
and $$bx+ay=d$$, then in order to solve -------(2)
we find (1) $$+$$ (2) and then (1) $$-$$ (2), we shall get
$$(a+b)x+(a+b)y=c+d$$
i.e. $$\displaystyle x+y =\frac{c+d}{a+b}$$
and $$(a-b)x-(a-b)y=c-d$$
i.e. $$x-y=\dfrac{c-d}{a-b}$$
To find $$x$$, (3)+(4) gives, $$2x=\dfrac{c+d}{a+b}+\dfrac{c-d}{a-b}$$
$$\Rightarrow \displaystyle x=\frac{1}{2} \left ( \frac{c+d}{a+b}+\frac{c-d}{a-b} \right )$$
To find $$y$$, (3)-(4) gives, $$y=\displaystyle \frac{1}{2} \left ( \frac{c+d}{a+b}-\frac{c-d}{a-b} \right )$$
Read the above passage carefully and mark the correct choice.

...view full instructions

Pair of Linear ...

Question 1

No solution

Many solutions

Two solutions

One solution.

Question 2

$$(2, 0)$$

$$(0, 3)$$

$$(3, 0)$$

$$(0, 2)$$

Question 3

$$(0, 0), (0, 4), (6, 2)$$

$$(0, 0), (4, 4), (0, 2)$$

$$(0, 0), (7, 7), (5, 2)$$

$$(0, 0), (4, 4), (6, 2)$$

Question 4

Rs $$15$$ and Rs $$8$$

Rs $$10$$ and Rs $$15$$

Rs $$12$$ and Rs $$10$$

Rs $$16$$ and Rs $$12$$

Question 5

$$x=1;\, \, y=0$$

$$x=3;\, \, y=2$$

$$x=7;\, \, y=3$$

$$x=2;\, \, y=5$$

Question 6

$$(0, 2)$$

$$(2, 0)$$

$$(3, 0)$$

$$(0, 3)$$

Question 7

No

Yes

Data Insufficient

None of these

Question 8

positive

negative

$$0$$

none of the above

Question 9

$$x=2, y=3$$

$$x=3, y=2$$

$$x=2, y=2$$

$$x=3, y=3$$

Question 10

intersecting lines

parallel lines

coincident lines

all the above

User

Question Analysis

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.