Question 183047
{{{ x/2  +  y/10  =  3}}} Start with the second equation.



{{{10(x/cross(2))+cross(10)(y/cross(10))=10(3)}}} Multiply EVERY term by the LCD {{{10}}} to clear any fractions.



{{{5x+y=30}}} Distribute and multiply.



So we have the system of equations:



{{{system(5x-3y=5,5x+y=30)}}}




{{{-1(5x+y)=-1(30)}}} Multiply the both sides of the second equation by -1.



{{{-5x-y=-30}}} Distribute and multiply.



So we have the new system of equations:

{{{system(5x-3y=5,-5x-y=-30)}}}



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



{{{(5x-3y)+(-5x-y)=(5)+(-30)}}}



{{{(5x-5x)+(-3y-y)=5+-30}}} Group like terms.



{{{0x-4y=-25}}} Combine like terms.



{{{-4y=-25}}} Simplify.



{{{y=(-25)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{y}}}.



{{{y=25/4}}} Reduce.



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{{{5x-3y=5}}} Now go back to the first equation.



{{{5x-3(25/4)=5}}} Plug in {{{y=25/4}}}.



{{{5x-75/4=5}}} Multiply.



{{{4(5x)-cross(4)(75/cross(4))=4(5)}}} Multiply EVERY term by the LCD {{{4}}} to clear any fractions.



{{{20x-75=20}}} Multiply.



{{{20x=20+75}}} Add 75 to both sides.



{{{20x=95}}} Combine like terms.



{{{x=95/20}}} Divide both sides by {{{20}}} to isolate {{{x}}}.



{{{x=19/4}}} Reduce.



So the solutions are {{{x=19/4}}} and {{{y=25/4}}}



Which form the ordered pair *[Tex \LARGE \left(\frac{19}{4},\frac{25}{4}\right)].



This means that the system is consistent and independent.