Question 175480


Start with the given system of equations:

{{{system(-3a+b=4,-9a+5b=-1)}}}



{{{-3(-3a+b)=-3(4)}}} Multiply the both sides of the first equation by -3.



{{{9a-3b=-12}}} Distribute and multiply.



So we have the new system of equations:

{{{system(9a-3b=-12,-9a+5b=-1)}}}



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



{{{(9a-3b)+(-9a+5b)=(-12)+(-1)}}}



{{{(9a+-9a)+(-3b+5b)=-12+-1}}} Group like terms.



{{{0a+2b=-13}}} Combine like terms. Notice how the x terms cancel out.



{{{2b=-13}}} Simplify.



{{{b=(-13)/(2)}}} Divide both sides by {{{2}}} to isolate {{{b}}}.



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{{{9a-3b=-12}}} Now go back to the first equation.



{{{9a-3(-13/2)=-12}}} Plug in {{{b=-13/2}}}.



{{{9a+39/2=-12}}} Multiply.



{{{2(9a+39/cross(2))=2(-12)}}} Multiply both sides by the LCD {{{2}}} to clear any fractions.



{{{18a+39=-24}}} Distribute and multiply.



{{{18a=-24-39}}} Subtract {{{39}}} from both sides.



{{{18a=-63}}} Combine like terms on the right side.



{{{a=(-63)/(18)}}} Divide both sides by {{{18}}} to isolate {{{a}}}.



{{{a=-7/2}}} Reduce.



So our answer is {{{a=-7/2}}} and {{{b=-13/2}}}.



Which form the ordered pair *[Tex \LARGE \left(-\frac{7}{2},-\frac{13}{2}\right)].



This means that the system is consistent and independent.