Question

How do you solve the simultaneous equations `4x+5y=0` and `8x-15y=5`?

Answer 1

`x=0.25` and `y=-0.2`

Explanation:

For simultaneous equations you have to know 2 rules:
• Same signs subtract
meaning if both equations have the same sign you subtract to cancel out `x or y`

•Different signs add
meaning if both equations have different signs you add to also cancel out `x or y`

In this case, you will add both equations because they are of different signs

`4x + 5y = 0`
`8x-15y=5`

multiply the first equation by `3` to cancel out `y` values by adding

after multiplying you'll have
`12x+15y=0`
`+`
`8x-15y=5`
now add both equations
`20x=5`
`x=5/20`
`x=0.25`

Substitute the value of `x` in either of the equations

`4x+5y=0`
`4(0.25)+5y=0`
`1+5y=0`
`5y=-1`
`y=-1/5` or `-0.2`

so `x=0.25` and `y=-0.2`