Question

How do you solve the system of equations `10x + 7y = - 9` and `- 5x - 3y = 6`?

Answer 1

Let's solve for `x`
`1^(st)` equation
`10x+7y=-9`
Transfer `7y`
`10x=-9-7y`
Divide it by 2
`5x=-(9+7y)/2`
`-5x=(9+7y)/2`
This `uarr` is just for the next equation.... take out the value of `x`
`10x=-9-7y`
`x=-(9+7y)/10`
`2^(nd)` equation
`-5x-3y=6`
Put value of `-5x`
`(9+7y)/2-3y==6`
LCM
`(9+7y)/2-(6y)/2=6`
That gives
`(9+y)/2=6`
Transfer 2
`9+y=12`
Transfer 9
`color(red)(y=3`
`x=-(9+7y)/10`
Put value of `y`
`x=-(9+7xx3)/10`
`x=-(9+21)/10`
`x=-30/10`
`color(red)(x=-3`