# Free Pair of Linear Equations in Two Variables 03 Practice Test - 10th Grade

### Question 1

If 3x=2y−2 is written in the standard form ax+by+c=0, what will be the possible values of a, b and c?

a = 1, b = -2 and c = 2

a = 3, b = -2 and c = 2

a = -3, b = -2 and c = 1

a = -3, b = 2 and c = -2

#### SOLUTION

Solution :B and D

The given equation is

3x=2y−2.

After rearranging the equation, we get

⇒3x−2y+2=0

On comparing the above equation with ax+by+c=0, we get

a = 3, b = -2 and c = 2

∴ The values of a, b and c are 3, -2 and 2 respectively.

But the equation can also be written as

(−1)×(3x−2y+2)=(−1)×0

⇒−3x+2y−2=0

On comparing the above equation with ax+by+c=0, we get

a = -3, b = 2 and c = -2

∴ The values of a, b and c are -3, +2 and -2 respectively.

Hence, we have two sets of values for a, b and c.

### Question 2

The line represented by the equation 4x+5y=10 intersects the y axis at (0, 2).

True

False

#### SOLUTION

Solution :A

The line intersects the y axis when the value of x coordinate is 0.

Thus, on y axis, x=0.

Substituting this value in the given equation:

⇒5y=10

⇒y=2

Thus, the line intersects the y axis at point (0,2).

### Question 3

54 is divided into two parts such that sum of 10 times the first part and 22 times the second part is 780. What is the bigger part?

34

32

30

24

#### SOLUTION

Solution :A

Let the 2 parts of 54 be x and y

x+y = 54 ....(i)

and 10x + 22y = 780 ...(ii)

Multiply (i) by 10 , we get

10 x + 10 y = 540 ...(iii)

Subtracting (ii) from (iii)

- 12y = - 240

y = 20

Subsituting y = 20 in x + y = 54 ,

⟹ x + 20 = 54

⟹x = 34Hence, x = 34 and y = 20

### Question 4

The lines that represent these two equations x+2y=5 and 4x+4y−6=0 meet at only one point (-2, 3.5). The pair of equations is

dependent

consistent

#### SOLUTION

Solution :B

A pair of linear equations in two variables which has a solution, is said to be consistent.

Here the lines representing the given linear equations are meeting only at point (-2, 3.5) giving a unique solution. Therefore, it is a consistent pair of linear equations.

Now, a pair of linear equations in two variables is said to be dependent when the lines representing them are coinciding i.e. will have many solutions.

Here, the lines have only one solution (-2, 3.5). Therefore, they aren't dependent.

### Question 5

Measure of one of the angles of a parallelogram is twice the measure of its adjacent angle. Then angles of the parallelogram are

60∘, 100∘, 180∘, 20∘

140∘, 20∘, 120∘, 80∘

60∘, 120∘, 60∘, 120∘

100∘, 80∘, 100∘, 80∘

#### SOLUTION

Solution :C

Let the measure of the angle be x and that of its adjacent angle be y.

x=2y ...(i) (given)

x+y=180∘ ...(ii)

(sum of adjacent angles of a parallelogram is 180∘)

On substituting (i) in (ii), we get

2y+y=180∘

⇒y=60∘

Since x=2y, x=120∘.

We know that opposite angles of parallelogram are equal.

⇒ Measure of the angles are 60∘, 120∘, 60∘ and 120∘.

### Question 6

Solving 52+x+1y−4=2; 62+x−3y−4=1,

we get

x =

y =

#### SOLUTION

Solution :Let, p = 12+x and q = 1y−4

Thus, given equations reduce to,

5p+q=2 ... (i)

6p−3q=1 ... (ii)

On multiplying (i) by 3 and then adding it to (ii), we get15p+3q=6

6p−3q=1_______________

21p=7

⇒p=13

and on substituting this value in (ii) we get

613−3q=1

⇒q=13

Now, p=12+x

⇒13=12+x

⇒x=1

We know that q=1y−4

⇒13=1y−4

⇒y=7

### Question 7

Which of the following are Pair of Linear Equation in two variables?

2x+y=2;3x−z=2

12x+4y+3=0;4x+4y+4=0

x+2=0;a+2b=0

x+y−3=0;4a+2b+c=24

#### SOLUTION

Solution :B

Two linear equations in same two variables are called pair of linear equation in two variables.

12x+4y+3=0 and 4x+4y+4=0

are linear equations in same two variables.

### Question 8

For the given linear equation y−3x+1=0, what are the values of y if x=[3,−4,2]?

5, -8, 13

8, 5, 13

8, 8, 8

8, -13, 5

#### SOLUTION

Solution :D

We have y−3x+1=0

For x=3

⇒y−3(3)+1=0

∴y=8

For x=−4

⇒y−3(−4)+1=0

∴y=−13

For x=2

⇒y−3(2)+1=0

∴y=5

Thus, the values of y if x=[3,−4,2] are 8, -13 and 5 respectively.

### Question 9

Find the point at which the line represented by the equation 6x+5y=9, intersects the x-axis.

(0,32)

(32,0)

(1,0)

(2,3)

#### SOLUTION

Solution :B

Let the line intersects at point (x, y).

We know that if a line intersects the x-axis then the y coordinate of the point at which it intersects will be 0.

⇒ y = 0

On substituting y = 0 in the given equation, we get

6x+0=9

⇒x=32

Thus, the point at which the given line intersects the x-axis is (32,0).

### Question 10

If the linear equation y=7x−4 is written in standard form, the standard form being ax+by+c=0, then what are the possible value of a,b,c?

a=−7,b=1,c=4

a=−7,b=−1,c=−4

a=7,b=−1,c=4

none of these

#### SOLUTION

Solution :A

The standard form of a linear equation is ax+by+c=0.

The given equation is y=7x−4.

It can be rewritten as −7x+y+4=0.

⇒a=−7,b=1 and c=4.

But the equation can also be written as,

7x−y−4=0.

⇒a=+7,b=−1 and c=−4.