Question

3/4x -1/2y= 8 and 2x +y=40

Answer 1

The value of x is 16 and the value of y is 8.

Explanation:

Consider the provided equation.

`(3)/(4)x -(1)/(2)y= 8\ and\ 2x +y=40`

Isolate x for
`\:(3)/(4)x-(1)/(2)y=8`

`(3)/(4)x-(1)/(2)y+(1)/(2)y=8+(1)/(2)y`

`(3)/(4)x=8+(1)/(2)y`

Multiply both side by 4 and simplify.

`3x=32+2y`

`x=(32+2y)/(3)`

Substitute the value of x in
`2x +y=40`

`2\cdot (32+2y)/(3)+y=40`

`(64)/(3)+(7y)/(3)=40`

`64+7y=120`

`7y=56`

`y=8`

Now substitute the value of y in
`x=(32+2y)/(3)`

`x=(32+2\cdot \:8)/(3)`

`x=16`

Hence, the value of x is 16 and the value of y is 8.