Question

solve the pair of linear equation x/6+y/15=4 & x/3-y/12=19/4​

Answer 1

Step-by-step explanation:

x/6 + y/15 =4.

x/3 - y/12 =19/4.

Multiply equation (x/6 + y/15 = 4) by 30 both Left hand side and right hand side.

Now if you multiply Left hand side by 30 we get

30*(x/6 + y/15)

= 30*x/6 + 30*y/15

=5x + 2y.

Now if we multiply Right hand side of the equation by 30 we get

4*30 = 120.

Now if we multiply Left hand side of the equation x/3 - y/12 =19/4 by 12 we get

12*(x/3-y/12)

=12*x/3-12*y/12

=4x-y.

Now if we multiply Right hand side of the equation by 12 we get

12*(19/4)

=3*19

=57.

Now we got two new equations 5x+2y =120 and 4x-y = 57

Now multiply the equation 4x-y = 57 by 2 Both Left hand side and Right hand side we get 2*(4x-y) = 2*57.

We get 8x-2y = 114.

Now if we add 5x + 2y = 120 and 8x-2y = 114 both Left hand side and Right hand side we get

5x+2y+8x-2y = 120 + 114

13x =234

So x = 234/13 = 18.

So if we substitute x= 18 in 5x+2y = 120

We get

5*18 +2y = 120

90 + 2y = 120

2y= 120-90

2y = 30

y = 15.

So x= 18 and y = 15.

Hope you understood.