Question 201006


Start with the given system of equations:

{{{system(2a+3b=-1,3a+5b=-2)}}}



{{{-3(2a+3b)=-3(-1)}}} Multiply the both sides of the first equation by -3.



{{{-6a-9b=3}}} Distribute and multiply.



{{{2(3a+5b)=2(-2)}}} Multiply the both sides of the second equation by 2.



{{{6a+10b=-4}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-6a-9b=3,6a+10b=-4)}}}



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(-6a-9b)+(6a+10b)=(3)+(-4)}}}



{{{(-6a+6a)+(-9b+10b)=3+-4}}} Group like terms.



{{{0a+b=-1}}} Combine like terms.



{{{b=-1}}} Simplify.



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{{{-6a-9b=3}}} Now go back to the first equation.



{{{-6a-9(-1)=3}}} Plug in {{{b=-1}}}.



{{{-6a+9=3}}} Multiply.



{{{-6a=3-9}}} Subtract {{{9}}} from both sides.



{{{-6a=-6}}} Combine like terms on the right side.



{{{a=(-6)/(-6)}}} Divide both sides by {{{-6}}} to isolate {{{a}}}.



{{{a=1}}} Reduce.



So the solutions are {{{a=1}}} and {{{b=-1}}}.