Question

How do you solve the system `-3(5+x)=y` and `5(x-3)=2y+4`?

Answer 1

The solution for the system of equations is:
`color(blue)( x = -1 , y =-12`

Explanation:

`-3(5+x)=y`
`-15 -3x = y`
`y +3x = -15` ............equation `(1)`

`5x-15=2y+4`
`5x - 2y = 4 +15`
`5x - color(blue)(2y) = 19`................equation `(2)`

• Multiplying equation `(1)` by `2`
  `y +3x = -15`
  `color(blue)( 2y)+6x = -30` ...........equation `(3)`
• Adding equations `2 and 3` to eliminate `color(blue)(2y)`

`5x - cancelcolor(blue)(2y) = 19`
`cancelcolor(blue)( 2y)+6x = -30`
`11x = -11`
`color(blue)(x = -1`

Substituting `x` in equation `(1)` to find `y`:
`y = -15-3x`
`y = -15-3.(-1)`
`color(blue)(y = -12`