Need help with basic system of equations with two unknown values

[Hivoyer]

Homework Statement

This is the problem:

|4(x+2) - 7(x-y) = 7
|7(x+y) + 10(x-2) = 79

I need to solve this, I'm not quite sure what to do, the operators in the brackets are different, so even if I multiply by -1, if the operator in front of one variable changes, the other one will change too, still making them incompatible with the bottom one.

Homework Equations

The Attempt at a Solution

I tried going the straight way by just doing all the operations until I get them to a simple as possible state:

|4(x+2) - 7(x-y) = 7
|7(x+y) + 10(x-2) = 79

into:

|4x + 7y + 1 = 0
|10x + 7y -99 = 0

This however doesn't get me anywhere.Could someone offer some help?(I know the problem sounds way too stupid :( )
Combining them gives me:

14x+ 14y - 98 = 0 ,which I turn into:
x + y - 7 = 0 , which still doesn't really get me anywhere, x + y = 7.The book says the answer is 5 and 2, but not sure how to solve it properly.

 

[SteamKing]

Why don't you expand out the brackets and collect like terms?
For instance:
4(x+2) - 7(x-y) = 7 turns into 4x + 8 - 7x - 7y = 7 turns into -3x - 7y = -1

 

[Hivoyer]

I think I solved it, is this correct:

I expanded the brackets as you said, but multiplied the bottom one with (-1), so I got this:

4x + 8 - 7x + 7y = 7
-7x - 7y - 10x +20 = -79

Then I collect them, so 7y and (-7y) are removed, leaving only X.

 

[SteamKing]

I'm not sure you understand: You have two simultaneous equations with unknowns x and y. You are supposed to determine the values of x and y which satisfy the equations.

 

[Hivoyer]

Yeah when only x is left I find it, then replaced it with the found value in the top formula to find y.

 

[Borek]

If I understand what is going on you are trying to add both equations side by side in such a way one of the unknowns cancels out. That's an OK method, but you can also use different approach - solve one of the equations for one unknown, and plug it into the other equation:

x+y=1
2x+y=3

From the first equation

y=1-x

plugging into the second

2x+1-x=3

collecting like terms

(2x-x)=3-2

or

x=1

and you have an equation in one unknown only (actually it got solved just by tidying it up).

And most likely you misunrderstood what SteamKing meant by "collect like terms" - he meant to combine together all expressions containing each unknown, and all free expressions. To quote his post again:

4(x+2) - 7(x-y) = 7 turns into 4x + 8 - 7x - 7y = 7 turns into -3x - 7y = -1

4x + 8 - 7x - 7y = 7

after grouping:

(4x - 7x) - 7y = (7 - 8)

and this directly yields

-3x - 7y = -1