Question

How do you solve the following system: # 1/2x - 2y = 4 , 5x+3y=-1 #?

Answer 1

`x = 20/23 and y = -41/23`

Explanation:

The approach is either to use substitution or elimination.

For substitution, you need to have a single variable such as `x`

`1/2x-2y =4" and "5x+3y =-1`

Multiply the first equation by `2`

`2xx1/2x -2xx2y =2xx 4`

`x-4y =8`

`color(blue)(x = (4y+8))" "`Substitute for `x` in the other equation:

`color(white)(ml.m)5color(blue)(x)+3y=-1`
`color(white)(mmm)darr`
`color(white)(m)5color(blue)((4y+8)) +3y=-1`

`20y+40 +3y =-1`

`23y = -1-40`

`23y = -41`

`y = (-41)/23`

Now find `x" by using " x = 4y+8`

`x = 4((-41)/23)+8`

`x = 20/23`

Substitute to check:

`5x +3y`

`5(20/23)+3(-41 /23)`

`=100/23-123/23`

`=-1`