How about I show you how to do the first one and then you can apply the same process to the other two?
Notice that the coefficient on y in the first equation is -1 and the
coefficient on y in the second equation is 1.
-1 and 1 are additive inverses, meaning that their sum is 0.
This is the key concept in this solution method.
We know that ifand , then we can say ,
therefore we can take the right sides of your two equations and add them and
that sum will be equal to the sum of the left sides, like this:
Now all we need to do is collect like terms:
, or just
Divide by the coefficient on x,
, and you have half of your solution.
Substitute this value for x into either of the original equations:
, and solve:
And the solution set to the system is the ordered pair (-2,-1).
Check your answer:
, True
, Also True
In both of your other problems, the coefficients on y are additive inverses,
so you can use the exact procedure illustrated above to solve them yourself.