Question

Solve the simutenous equations (a) 2y=3x -13, 5x - 6y=23 (b) X=2y + 11, 4x + 3y=0 ?

Answer 1

a. `(4,-1/2)`
b. `(3,-4)`

Explanation:

a.
Rearrange the first equation to find `y` in terms of `x`
`y=(3x-13)/2`

Put this into the other equation:
`5x-6((3x-13)/2)=23`
`5x-9x+39=23`
`-4x=-16`
`x=-16/-4=4`

Putting 4 into the original equation:
`y=(3(4)-13)/2=-1/2`

`(4,-1/2)`

b.
We already have `x` in terms of `y` so we subtitute in:
`4(2y+11)+3y=0`
`8y+44+3y=0`
`11y=-44`
`y=-44/11=-4`

Putting back in:
`4x=-3y`
`4x=12`
`x=12/4=3`

`(3,-4)`