Question

Is the ordered pair (2,2) a solution to the system 2x - y = 2 and x + 3y =8?

Answer 1

Yes; `(x,y)=(2,2)` is a solution to
`color(white)("XXX")2x-y=2` and
`color(white)("XXX")x+3y=8`

Explanation:

Substituting `(color(red)(2),color(blue)(2))` for `(color(red)(x),color(blue)(y))`

1. in the expression `2color(red)(x)-color(blue)(y)`
   gives `(2xxcolor(red)(2))+color(blue)(2) = 2`
   So `(color(red)(2),color(blue)(2))` is a solution for `2color(red)(x)-color(blue)(y)=2`
2. in the expression `color(red)(x)+3color(blue)(x)`
   gives `color(red)(2)+(3xxcolor(blue)(2))=8`
   So `(color(red)(2),color(blue)(2))` is a solution for `color(red)(x)+3color(blue)(y)=8`

Since `(color(red)(2),color(blue)(2))` is a solution for both equations,
it is a solution for the system of equations (since the system is comprised of only those two equations).