Question

How do you solve the following linear system: `{(4x + 5y = -3) ,( y = 1/2x - 3/2):}`?

Answer 1

See explanation.

Explanation:

You can solve the equation by replacing `y` in the first equation with `1/2x-3/2` from the second equation:

`{(4x+5(1/2x-3/2)=-3),(y=1/2x-3/2):}`

`{(4x+5/2x-15/2=-3),(y=1/2x-3/2):}`

Now we can calculate `x` from the first equation:

`{(13/2x=-3+15/2),(y=1/2x-3/2):}`

`{(13/2x=9/2),(y=1/2x-3/2):}`

`{(13x=9),(y=1/2x-3/2):}`

`{(x=9/13),(y=9/26-3/2):}`

Last step is to put the calculated value of `x` into the second equation to calculate `y`:

`{(x=9/13),(y=9/26-39/26):}`

`{(x=9/13),(y=-1 2/13):}`