Answer:
(x, y) = (6, -2)
Explanation:
I find it easiest to simplify the first equation by removing a factor of 4 from all terms. Doing that, it becomes ...
x + y = 4
Now, it can be subtracted from the second equation to eliminate the x-variable.
(x +6y) -(x +y) = (-6) -(4)
5y = -10 . . . . . . simplify
y = -2 . . . . . . . . divide by 5
Put this value in the simplified equation 1 above:
x + (-2) = 4
x = 6 . . . . . . . add 2
The solution (x, y) is (6, -2).
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There are other ways to solve this. I like graphing, as it is often quick and easy. It shows the solution is (6, -2).
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You can also use substitution. The second equation suggests an expression for x:
x = -6-6y . . . . subtract 6y
Now, this can be substituted into the first equation:
4(-6-6y) +4y = 16
-24 -24y +4y = 16 . . . . . . eliminate parentheses
-20y = 40 . . . . . . . . . . . . add 24 and simplify
y = -2 . . . . . . . . . . . . . . . . divide by -20
Then we can use the same expression for x that we substituted:
x = -6 -6(-2) = -6 +12 = 6
So, the solution is (x, y) = (6, -2).
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The rule of equations is that whatever you do to one side must also be done to the other side. If you add something to one side, the same value must be added to the other side. The same goes for subtraction, multiplication, and division, and for any application of functions, such as square root.
Another rule that is useful is that anything can be substituted by its equal. Equal things are always interchangeable.