Question

How do you solve the system `x= 3y-1` and `x+2y=9`?

Answer 1

Arrange the equations. You get `x=5` and `y=2`

Explanation:

`x-3y = -1`
`-x-2y = -9`

(after multiplying the 2nd equation by -1#

Now add these:
`-5y=-10`

`y=2`

Put this value in the 1st original equation:
`x-(3times2) = -1`
`x-6 = -1`
`x=-1+6`
`x=5`

Answer 2

`(x,y)to(5,2)`

Explanation:

`x=3y-1to(1)`

`x+2y=9to(2)`

`"rearrange equation "(2)" to give x in terms of y"`

`rArrx=9-2yto(3)`

`"since "(1)" and "(3)" both give x in terms of y we"`
`"can equate the right sides"`

`rArr3y-1=9-2y`

`"add 2y to both sides"`

`3y+2y-1=9cancel(-2y)cancel(+2y)`

`rArr5y-1=9`

`"add 1 to both sides"`

`rArr5y=10rArry=2`

`"substitute "y=2" in either "(1)" or "(3)`

`(1)tox=6-1=5`

`"solution is "(x,y)to(5,2)`