Question

How do you solve the system using the elimination method for 2a + 3b = 6 and 5a + 2b – 4 = 0?

Answer 1

`(a,b) = (0,2)`
`color(white)("XXXX")` `color(white)("XXXX")`(using elimination method)

Explanation:

[1]`color(white)("XXXX")` `2a+3b = 6`
[2]`color(white)("XXXX")` `5a+2b-4=0`

Rewite [2] into standard form:
[3]`color(white)("XXXX")` `5a+2b=4`

Multiply [1] by 2 and [3] by 3 to make the coefficients of `b` the same in both.
[4]`color(white)("XXXX")` `4a+6b=12`
[5]`color(white)("XXXX")` `15a+6b=12`

Subtract [4] from [5]
[6]`color(white)("XXXX")` `11a = 0`
Divide by 11
[7]`color(white)("XXXX")` `a=0`

Substitute `0` for `a` in [1]
[8]`color(white)("XXXX")` `2(0) + 3b = 6`
Simplify
[9]`color(white)("XXXX")` `b=2`