Question

Solve the following....

`5x+3y=7\\3x-5y=-23`

Answer 1

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

let's solve ~

The given equations are :

`\qquad \tt \dashrightarrow \:5x + 3y = 7 \: \: \: \: \: \: \: \: \: \: \: \: - (1)`

and

`\qquad \tt \dashrightarrow \:3x - 5y = - 23 \: \: \: \: \: \: - (2)`

Now, let's multiply equation (1) by 5 and equation (2) by 3 ~

we will get the results as :

`\qquad \tt \dashrightarrow \:25x + 15y = 35 \: \: \: \: - (3)`

`\qquad \tt \dashrightarrow \:9x - 15y = - 69 \: \: \: - (4)`

Now, add equation (3) and (4) :

`\qquad \tt \dashrightarrow \:25x + \cancel{ 15y} + 9x - \cancel{15y }= 35 + ( - 69)`

`\qquad \tt \dashrightarrow \:34x = - 34`

`\qquad \tt \dashrightarrow \:x = - 1`

Now, since we got the value of x, let's evaluate y~ by using equation (1) :

`\qquad \tt \dashrightarrow \:5x + 3y = 7`

`\qquad \tt \dashrightarrow \:5( - 1)+ 3y = 7`

`\qquad \tt \dashrightarrow \:3y - 5 = 7`

`\qquad \tt \dashrightarrow \:3y = 12`

`\qquad \tt \dashrightarrow \:y = 4`

Hence, value of y is 4

I hope you understood the whole procedure ~