Question

Solve the system of equations:10x+y=-180=5x+3y+4

Answer 1

First clear one variable of any equation, I will choose the x from the first:

`10x+y=-18`
`10x=-18-y`
`x=(-18-y)/(10)`

Now replace in the second:

`0=5x+3y+4`
`0=5((-18-y)/(10))+3y+4`
`5\left((-18-y)/(10)\right)+3y+4=0`
`5\cdot (-18-y)/(10)+3y+4-4=0-4`
`5\cdot (-18-y)/(10)+3y=-4`
`-9+(5y)/(2)=-4`
`-9\cdot \:2+(5y)/(2)\cdot \:2=-4\cdot \:2`
`-18+5y=-8`
`-18+5y+18=-8+18`
`5y=10`
`y=2`

Now replace first the y:

`x=(-18-y)/(10)`
`x=(-18-2)/(10)`
`x=(-20)/(10)`
`x=-2`

x=-2

y=2