Question

The linear combination method gives a solution of (–4, 2) for which of these systems of linear equations?

Answer 1

`3x + 13y = 14`

`6x + 11y = -2`

Explanation:

See Attachment for complete question

To determine which of the options has (-4,2) as its solution; we have to test each linear combination until we arrive at an answer;

Given that

`(x,y) = (-4,2)`

Testing Option A

`3x + 13y = 14`

`6x + 11y = -2`

Substitute
`x = -4` and
`y = 2` in
`3x + 13y = 14`

`3(-4) + 13(2) = 14`

Open Brackets

`-12 + 26 = 14`

`14 = 14`

Substitute
`x = -4` and
`y = 2` in
`6x + 11y = -2`

`6(-4) + 11(2) = -2`

Open Brackets

`-24 + 22 = 2`

`2 = 2`

In both cases, the expression on the right hand side equates to that on the left hand side;

Hence, there's no need to check for other options.