Question

How do solve the following linear system?: `x + y = 2, 3x + 2y = 12`?

Answer 1

Elimination is my favorite

Explanation:

( `x+y = 2` ) `*2` (Times the equation by two)

`2x+2y = 4`

Now subtract the equalities:
`color(blue)(3x)+color(red)(cancel(2y))= color(green)12`
`color(blue)(2x)+color(red)(cancel(2y))= color(green)4`
`color(blue)(x) + color(red)(0y)= color(green)8`

so `x = 8`

Thus, `y = -6` (by plugging `x=8` into an original equation)