SOLUTION: what is the linear combination of 2x-y=-3 -5x+y=9 would you also provide two more answers for me. 2x-3y=-16 x+3y=10 and 10x-5y=5 2x+5y=-5 thats all thanks for the help i

Algebra ->  College  -> Linear Algebra -> SOLUTION: what is the linear combination of 2x-y=-3 -5x+y=9 would you also provide two more answers for me. 2x-3y=-16 x+3y=10 and 10x-5y=5 2x+5y=-5 thats all thanks for the help i      Log On


   



Question 138398: what is the linear combination of
2x-y=-3
-5x+y=9
would you also provide two more answers for me.
2x-3y=-16
x+3y=10
and
10x-5y=5
2x+5y=-5
thats all thanks for the help i realy need it!

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

How about I show you how to do the first one and then you can apply the same process to the other two?

2x-y=-3
-5x%2By=9

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 if a=b and c=d, then we can say a%2Bc=b%2Bd,
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:

%282x-y%29%2B%28-5x%2By%29=-3%2B9

Now all we need to do is collect like terms:

-3x%2B0y=6, or just -3x=6

Divide by the coefficient on x,

x=-2, and you have half of your solution.

Substitute this value for x into either of the original equations:

2%28-2%29-y=-3, and solve:
-4-y=-3
-y=-3%2B4
-y=1
y=-1

And the solution set to the system is the ordered pair (-2,-1).

Check your answer:
2%28-2%29-%28-1%29=-4%2B1=-3, True
-5%28-2%29%2B%28-1%29=10-1=9, 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.