Question

Where does `2x+y=1` and `9x+3y=-3` intersect?

Answer 1

By substitution method,

you take one equation and keep a variable on one side and all other variable as well as the independent terms to the other.

`2x + y = 1`
`y = 1 - 2x` ......... equation (1)

Now replace this value of y in the other equation,

`9x+3y=-3`
`9x + 3 ( 1 - 2x ) = -3`
`9x + 3 - 6x` = `-3`
`3x` = `-3-3`
So,
`x` = -2

Now replace this value of `x` in equation (1) ,
So, `y = 1 - 2*(-2)`
Therefore,
`y = 5`

So, the two lines intersect at ( -2, 5 )