Question

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Solve the simultaneous equations: a) x + y = 7, 3x - 2y = 11 b) 7x - 2y = 1, 3x + 4y = 15?

Solve the simultaneous equations:

a) x + y = 7, 3x - 2y = 11

b) 7x - 2y = 1, 3x + 4y = 15

Expert Solution

Solution:

a) We have:

x + y = 7

or, y = 7 - x - Eq. I

3x - 2y = 11 - Eq. II

Substitute value of y from Eq. I in Eq. II:

3x - 2 (7 - x) = 11

⇒ 3x - 14 + 2x = 11

⇒ 5x = 11 + 14 = 25

⇒ x = 25/5 = 5

Substitute x = 5 in Eq. I:

y = 7 - 5 =3

Thus, the solution of given equations is: x = 5, y = 2

a) We have:

7x - 2y = 1 - Eq. I

3x + 4y = 15 - Eq. II

Multiplying Eq. I by 2:

14x - 4y = 2 - Eq. III

Adding Eq. II and Eq. III:

17x = 17

⇒ x = 17/17 = 1

Substitute x = 1 in Eq. I:

7 (1)- 2y = 1

⇒ 7 - 1 = 2y

⇒ y = 6/2

Thus, the solution of given equations is: x = 1, y = 3

Thus, the solution of given equations is: a) x = 5, y = 2 and b) x = 1, y = 3

Shams answered 2 years ago

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