Question

How do you solve the system using the elimination method for 4x-y=9 and x-3y=16?

Answer 1

`(x,y) = (1,-5)`

Explanation:

[1]`color(white)("XXXX")` `4x-y=9`
[2]`color(white)("XXXX")` `x-3y = 16`

Multiply [2] by 4 to obtain the same coefficient of `x` as in [1]
[3]`color(white)("XXXX")` `4x-12y = 64`

Subtract [1] from [3]
[4]`color(white)("XXXX")` `-11y = 55`

Solve for `y`
[5]`color(white)("XXXX")` `y= -5`

Substitute `y=-5` back into [1]
[6]`color(white)("XXXX")` `4x - (-5) = 9`

Solve for `x`
[7]`color(white)("XXXX")` `4x = 4`

[8]`color(white)("XXXX")` `x = 1`