Question

How do you solve `2c - d = - 2` and `4c + d = 20`?

Answer 1

`(c,d)=(3,8)`

Explanation:

Given:
`[1]color(white)("XXX")2c-d=-2`
`[2]color(white)("XXX")4c+d=20`

Add [1] and [2]
#{: (,color(white)("XXX"),2c,-d,=,-2), (+,,4c,+d,=, 20), (,,"-------","-----","----","-----"), ([3],,6c,,=,18) :}#

Divide [3] by `6`
`[4]color(white)("XXXXXX")c = 3`

Substitute `3` (from [4]) for `c` in [1]
`[5]color(white)("XXX")2*(3)-d = -2`
Simplify
`[6]color(white)("XXX")6-d = -2`
Subtract `6` from both sides
`[7]color(white)("XXX")-d = -8`
Multiply both sides by `(-1)`
`[8]color(white)("XXX")d=8`