Pair of Linear Equations Final Assessment

Section A: Core Concepts

Question 1mcq

Which is the standard form of

y=3x-2

?

A.

3x-y-2=0

B.

3x+y-2=0

C.

x-3y-2=0

D.

3x-y+2=0

Question 2mcq

For

x+2y=10

, if

x=4

, what is

y

?

A.

3

B.

2

C.

4

D.

6

Question 3mcq

Which point lies on the line

3x+y=12

?

A.

(2,6)

B.

(3,2)

C.

(4,1)

D.

(1,6)

Question 4mcq

If two plotted lines meet at

(2,-1)

, what does this point represent?

A.The common solution

B.Only the

x

-intercept

C.Only the

y

-intercept

D.The slope of both lines

Question 5mcq

A consistent pair with exactly one solution is represented by:

A.intersecting lines

B.parallel lines

C.coincident lines

D.curved lines

Question 6mcq

Which condition shows no solution for

a_1x+b_1y+c_1=0

and

a_2x+b_2y+c_2=0

?

A.

\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}

B.

\frac{a_1}{a_2}\ne\frac{b_1}{b_2}

C.

\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}

D.

a_1=b_1=c_1

Section B: Graphical and Consistency Reasoning

Question 7mcq

Which pair has infinitely many solutions?

A.

3x-2y=6

and

6x-4y=12

B.

3x-2y=6

and

6x-4y=15

C.

x+y=5

and

x-y=1

D.

2x+y=4

and

x+2y=4

Question 8mcq

Find

k

if

kx+6y=15

and

2x+3y=9

have no solution.

A.

4

B.

2

C.

5

D.

3

Question 9mcq

Solve

x-y=4

and

y=2x-11

.

A.

(7,3)

B.

(3,7)

C.

(5,1)

D.

(9,5)

Question 10mcq

Which equation is easiest to isolate a variable from in the pair

5x+y=13

and

3x-2y=4

?

A.

5x+y=13

, isolate

y

B.

3x-2y=4

, isolate

x

C.Both require equal work

D.Neither can be used for substitution

Question 11mcq

Solve

x+2y=11

and

x-y=2

.

A.

(5,3)

B.

(3,5)

C.

(7,2)

D.

(4,4)

Question 12mcq

To eliminate

x

in

2x+5y=16

and

3x-4y=1

, what should you multiply by?

A.First by

3

, second by

2

B.First by

2

, second by

3

C.Both by

5

D.First by

4

, second by

5

Section C: Application and Modelling

Question 13mcq

The cost of

3

pencils and

2

erasers is

₹26

. The cost of

2

pencils and

4

erasers is

₹28

. Which pair models the situation?

A.

3p+2e=26

,

2p+4e=28

B.

3p+2e=28

,

2p+4e=26

C.

5p+6e=54

,

p-e=2

D.

3p-2e=26

,

2p-4e=28

Question 14mcq

A boat goes

30

km downstream in

2

h and

18

km upstream in

3

h. What are the boat speed in still water and stream speed?

A.Boat

10.5

km/h, stream

4.5

km/h

B.Boat

12

km/h, stream

3

km/h

C.Boat

9

km/h, stream

6

km/h

D.Boat

15

km/h, stream

6

km/h

Question 15mcq

Which pair verifies

(1,4)

as a solution?

A.

x+y=5

and

2x+y=6

B.

x+y=4

and

2x+y=5

C.

x-y=5

and

x+y=6

D.

2x+2y=8

and

x+y=6

Question 16mcq

In a money problem, a student uses

x

for number of notebooks but writes

60x

for pens costing

₹60

each. What is the issue?

A.The variable does not match the item being priced.

B.The price should be divided by

60

.

C.The total must always be

x+60

.

D.There is no issue.

Question 17mcq

For

2x+ay=8

and

4x+6y=16

to be coincident, find

a

.

A.

3

B.

6

C.

2

D.

4

Question 18mcq

A class collected

₹2200

in

100

notes and

50

notes. There were

28

notes in all. How many

₹100

notes were there?

A.

16

B.

12

C.

14

D.

18

Section D: Mixed Challenge

Question 19mcq

A student converts “twice the larger number is

6

more than the smaller” into

2y=x+6

, where

x

is larger and

y

is smaller. What is wrong?

A.It should be

2x=y+6

.

B.It should be

x+2y=6

.

C.It should be

2x+2y=6

.

D.There is no error.

Question 20mcq

A graph shows the lines

x+y=8

and

x-y=2

intersecting. Which point should appear as their intersection?

A.

(5,3)

B.

(3,5)

C.

(8,2)

D.

(2,8)

Question 21mcq

Solve

5x-2y=1

and

3x+2y=15

.

A.

(2,\frac{9}{2})

B.

(\frac{9}{2},2)

C.

(2,5)

D.

(3,3)

Question 22mcq

What should be done first to eliminate

y

from

4x+7y=25

and

6x-5y=9

?

A.Multiply first by

5

and second by

7

B.Multiply first by

7

and second by

5

C.Add directly

D.Subtract directly

Question 23mcq

A parking lot has cars and bikes. There are

35

vehicles and

100

wheels. If cars are

c

and bikes are

b

, which equations are correct?

A.

c+b=35

,

4c+2b=100

B.

c+b=100

,

4c+2b=35

C.

4c+b=35

,

c+2b=100

D.

2c+4b=100

,

c-b=35

Question 24mcq

Using

c+b=35

and

4c+2b=100

for cars and bikes, how many cars are there?

A.

15

B.

20

C.

10

D.

25