Question

How do you solve the system using the elimination method for 3a + 4b = 2 and 4a - 3b = -14?

Answer 1

`(a,b) = (-2,2)`

Explanation:

Given
[1]`color(white)("XXXX")` `3a+4b=2`
[2]`color(white)("XXXX")` `4a-3b = -14`

Multiply [1] by 4 and [2] by 3 to obtain two equations with the same `a` coefficient
[3]`color(white)("XXXX")` `12a+16b = 8`
[4]`color(white)("XXXX")` `12a-9b=-42`

Subtract [4] from [3] to clear the `a` term
[5]`color(white)("XXXX")`25b= 50#

Divide both sides by `25`
[6]`color(white)("XXXX")` `b =2`

Substitute `b=2` into equation [1]
[7]`color(white)("XXXX")` `3a+4(2) = 2`

[8]`color(white)("XXXX")` `3a = -6`

[9]`color(white)("XXXX")` `a = -2`