Practice Set 1.1

Complete the following activity to solve the simultaneous equations. 5x + 3y = 9 . (i)…

3a + 5b = 26; a + 5b = 22 Solve the following simultaneous equation.…

x + 7y = 10; 3x - 2y = 7 Solve the following simultaneous equation.…

2x - 3y = 9; 2x + y = 13 Solve the following simultaneous equation.…

5m - 3n = 19; m - 6n = -7 Solve the following simultaneous equation.…

5x + 2y = -3; x + 5y = 4 Solve the following simultaneous equation.…

1/3 x+y = 10/3 2x + 1/4 y = 11/4 Solve the following simultaneous equation.…

99x + 101 y = 499; 101x + 99y = 501 Solve the following simultaneous equation.…

49x - 57y = 172; 57x - 49y = 252 Solve the following simultaneous equation.…

###### Practice Set 1.1

Question 1.Complete the following activity to solve the simultaneous equations.

5x + 3y = 9 ……. (i)

2x + 3y = 12 ……… (ii)

Answer:

5x + 3y = 9 ……. (i)

2x + 3y = 12 ……… (ii)

Subtracting equation (ii) from (i), we get,(5x + 3y ) - (2x + 3y) = 9 - 12

5x - 2x + 3y - 3y = -3

3x = -3

x = -1

Putting the value of x in equation (i),

5(-1) + 3y = 9

-5 + 3y = 9

3y = 14

y = 14/3

Let’s add equations (I) and (II).

Hence, x = -1 and y = 14/3 is the solution of the equation.

Question 2.

Solve the following simultaneous equation.

3a + 5b = 26; a + 5b = 22

Answer:

Change the sign of Eq. (II)

Substituting a = 2 in Eq. (II)

∴ solution is (a, b) = (2, 4)

Question 3.

Solve the following simultaneous equation.

x + 7y = 10; 3x – 2y = 7

Answer:

Multiply Eq. I by 2 and Eq. II by 7

x=3

Substituting x= 3 in Eq. I

7y=7

y=1

∴ Solution is (x , y) = (3, 1)

Question 4.

Solve the following simultaneous equation.

2x – 3y = 9; 2x + y = 13

Answer:

Change the sign of Eq. (II)

Substituting y = 1 in Eq. (II)

2x = 13 - 1

2x = 12

x = 6

∴ solution is (x, y) = (1,6)

Question 5.

Solve the following simultaneous equation.

5m – 3n = 19; m – 6n = –7

Answer:

Multiply Eq. II by 5

equating (I) and (III), change the sign of Eq. (III)

Adding both we get

⇒

⇒

⇒ n = 2

Substituting n = 2 in Eq 1

⇒ 5m - 3(2) = 19

⇒ 5m - 6 = 19

⇒ 5m = 25

⇒ m = 5

∴ Solution is (m , n) = (5, 2)

Question 6.

Solve the following simultaneous equation.

5x + 2y = –3; x + 5y = 4

Answer:

Multiply Eq. I by 5 and Eq. II by 2

Change sign of Eq.(IV)

Subsituting x=–1in Eq.II

∴ solution is (x, y) = (–1, 1)

Question 7.

Answer:

⇒ ⇒

⇒ ⇒

Multiplying Eq. II by 3

Equating Eq. I and III, change the signs of Eq. III

Substituting x = 1 in Eq. I

∴ solution is (x,y) = (1, 3)

Question 8.

Solve the following simultaneous equation.

99x + 101 y = 499; 101x + 99y = 501

Answer:

Adding both the Equations

Dividing both sides by 200

…(III)

Subtract equation (I) and (II)

Divide both sides by (–2)

…(IV)

Equating Eq. (III) and (IV)

Substituting x=3 in Eq. III

∴ solution is (x, y) = (3, 2)

Question 9.

Solve the following simultaneous equation.

49x – 57y = 172; 57x – 49y = 252

Answer:

Adding both the Equations

Dividing both sides by 106

…(III)

Subtract equation (I) and (II)

Divide both sides by (–8)

…(IV)

Equating Eq. (III) and (IV)

Substituting x=7 in Eq. IV

∴ solution is (x, y) = (7,3)