Question

How do you solve the following linear system: # 2x + 3y = 2, x + 6y = 4, #?

Answer 1

`(x,y)=color(green)(""(0,2/3))`

Explanation:

Given:
[1]`color(white)("XXX")2x+3y=2`
[2]`color(white)("XXX")x+6y=4`

[1]`xx 2`
`color(white)("XXX")`[3]`color(white)("XXX")4x+6y=4`

[3]`-` [2]
`color(white)("XXX")`[4]`color(white)("XXX")3x=0`

[4]`div 3`
`color(white)("XXX")`[5]`color(white)("XXX")x=0`

Substituting (from [5]) `0` for `x` in [2]
`color(white)("XXX")`[6]#color(white)("XXX")0+6y=4

[6]`div 6`
`color(white)("XXX")`[7]`color(white)("XXX")y=2/3`

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For verification purposes, you should check this result by substituting
`x=0` and `y=2/3` back into equation [1].