Question

`[tex]\left \{ {{3x+4y=36} \atop {y=-(1)/(2) x+8}} \right.`

Answer 1

`\qquad \qquad \huge \underline{\boxed{ \sf {Answer}}}`

Let's solve ~

The given equations are :

`\qquad \dashrightarrow \bf \: 3x + 4y = 36 \sf \: \: \: \: \: \: \: \: \: \: (1)`

and

`\qquad \dashrightarrow \sf \:y = - (1)/(2) x + 8`

[ multiply each sides by 2 ]

`\qquad \dashrightarrow \sf \: 2y = - x + 16`

`\qquad \dashrightarrow \sf \:x + 2y = 16`

[ multiply both sides by 2 ]

`\qquad \dashrightarrow \bf \: 2x + 4y = 32 \: \: \: \: \: \: \: \: \: \: \: \sf(2)`

Now, subtract equation (2) from (1)

`\qquad \dashrightarrow \sf \: 3x + 4y - (2x + 4y) = 36 - 32`

`\qquad \dashrightarrow \sf \: 3x + \cancel{4y }- 2x - \cancel{4y }= 4`

`\qquad \dashrightarrow \bf \: x = 4`

Now, as we got the value of x, let's solve for y :

`\qquad \dashrightarrow \sf \: y = - (1)/(2) x+ 8`

`\qquad \dashrightarrow \sf \: y = -(1)/(2) (4)+8`

`\qquad \dashrightarrow \sf \: y = - 2 + 8`

`\qquad \dashrightarrow \bf \: y = 6`