Question 138398
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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+y=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+c=b+d}}},
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:


{{{(2x-y)+(-5x+y)=-3+9}}}


Now all we need to do is collect like terms:


{{{-3x+0y=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(-2)-y=-3}}}, and solve:
{{{-4-y=-3}}}
{{{-y=-3+4}}}
{{{-y=1}}}
{{{y=-1}}}


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


Check your answer:
{{{2(-2)-(-1)=-4+1=-3}}}, True
{{{-5(-2)+(-1)=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.