Question

How do you solve the following system?: `-1/2x+5y=-20 , -x+6y=7`

Answer 1

Answer: `(-155/2 , -47/2)`

Explanation:

Equation 1: `-1/2 x + 5y = -20`

Equation 2: `-x + 6y = 7`

Multiply equation 1 by `-2` to eliminate fraction
`-2[-1/2x +5y =-20}] hArr` `color(red)(x -10y = 40)`

Take equation 2, solve for `x`

`-x+6y = 7 hArr color(red)(6y-7=x)`

Substitute `color(red)(6y-7=x)` into first equation

`color(red)(6y-7)-10y = 40`

`-4y= 47`

`color(blue)(y= -47/4)`

Substitute
`6(-47/4)-7= x`

`-141/2 -14/2 = x`

`color(blue)(-155/2 = x)`