Question

Solve the following pair of equations: x − 3y − 7 = 0 ; 3x − 5y − 15 = 0

Answer 1

EXPLANATION.

Equation are =

=> x - 3y - 7 = 0 .....(1)

=> 3x - 5y - 15 = 0 ......(2)

From equation (1) and (2) we get,

=> multiply equation (1) by 3

=> multiply equation (2) by 1

we get,

=> 3x - 9y - 21 = 0

=> 3x - 5y - 15 = 0

we get,

=> -4y = 6

=> y = - 3/2

put the value of y = - 3/2 in equation (1)

we get,

=> x - 3( - 3/2) - 7 = 0

=> x + 9/2 - 7 = 0

=> x = 7 - 9/2

=> x = 14 - 9 / 2

=> x = 5/2

Therefore,

value of x = 5/2 and y = -3/2

Answer 2

Given ,

The two equations are

★ x - 3y = 7 --- (i)

★ 3x − 5y = 15 --- (ii)

Multiply eq (i) by 3 , we get

3x - 9y = 21 --- (iii)

Subtract eq (ii) from eq (iii) , we get

3x - 9y - (3x - 5y) = 21 - 15

5y - 9y = 6

-4y = 6

y = -6/4

y = -3/2

Put y = -3/2 in eq (i) , we get

x - 3(-3/2) = 7

x + 9/2 = 7

2x + 9 = 14

2x = 5

x = 5/2

$\therefore$ The required values of x and y are 5/2 and -3/2