Question

How do you solve the system of equations `5x + 5y = 15` and `4x + 6y = 10`?

Answer 1

Solution set: `S = {4,-1}`

Explanation:

Its way more easy to simplify the system before work with, so:
`5x + 5y = 15` becomes `x+y =3` and
`4x+6y = 10` becomes `2x+3y=5`. Now, we isolate one term in the first equation: `x = 3-y` and put it in the second one:
`2(3-y) +3y = 5`, and the walk-through for solve it:
`-2y + 6 + 3y = 5`
`y = -1`
`y = -1`. With `y`'s value, now we go back to the first equation, as we left it, and solve it: `x = 3 -(-1) = 4`.
So, the solution set is: `S = {4,-1}`