Pair of Linear Equations Practice 2: Substitution and Elimination

Section A: Algebraic Methods

Question 1mcq

Using substitution, solve

x+y=9

and

x=4

. What is

y

?

A.

5

B.

4

C.

9

D.

13

Question 2mcq

Solve by substitution:

y=2x+1

and

x+y=10

.

A.

(3,7)

B.

(7,3)

C.

(4,5)

D.

(2,5)

Question 3mcq

For the pair

x=3y-2

and

2x+y=19

, which first step is most efficient?

A.Substitute

x=3y-2

into

2x+y=19

B.Multiply both equations by

3

C.Subtract the second equation from the first

D.Convert both equations to decimals

Question 4mcq

A student solves

4x+y=17

and

y=5-x

. Which substitution avoids fractions and extra rearranging?

A.Replace

y

by

5-x

in

4x+y=17

B.Solve

4x+y=17

for

x

first

C.Divide both equations by

y

D.Add the equations without substitution

Question 5mcq

In

3x+2y=16

and

3x-y=7

, which operation eliminates

x

?

A.Subtract the second equation from the first

B.Add the equations

C.Multiply both by

3

D.Divide the first by

2

Question 6mcq

Solve

2x+3y=13

and

2x-y=5

by elimination.

A.

(\frac{7}{2},2)

B.

(4,\frac{5}{3})

C.

(5,1)

D.

(2,3)

Section B: Check and Choose

Question 7mcq

Before eliminating

y

from

2x+3y=12

and

5x-2y=1

, what is a good scaling step?

A.Multiply the first equation by

2

and the second by

3

B.Multiply both equations by

5

C.Divide both equations by

y

D.Multiply the first equation by

3

only

Question 8mcq

For

7x-4y=2

and

3x+2y=20

, which scaled pair is ready to eliminate

y

by addition?

A.

7x-4y=2

and

6x+4y=40

B.

14x-8y=4

and

3x+2y=20

C.

21x-12y=6

and

6x+4y=40

D.

7x-4y=2

and

3x-2y=20

Question 9mcq

Which pair

(x,y)

is a solution of both

x+2y=11

and

3x-y=5

?

A.

(3,4)

B.

(5,3)

C.

(1,5)

D.

(4,3)

Question 10mcq

A student claims

(2,5)

solves

4x-y=3

and

x+y=7

. What is the best check?

A.It solves both equations, so the claim is correct.

B.It solves only

x+y=7

, so the claim is wrong.

C.It solves only

4x-y=3

, so the claim is wrong.

D.It solves neither equation.