Question 202425
{{{0.05x+0.25y=11}}} Start with the first equation. 



{{{100(0.05x)+100(0.25y)=100(11)}}} Multiply EVERY term by 100 to make every value a whole number. 



{{{5x+25y=1100}}} Multiply.


-------------------------------


{{{0.15x+0.05y=12}}} Move onto the second equation.



{{{100(0.15x)+100(0.05y)=100(12)}}} Multiply EVERY term by 100 to make every value a whole number. 



{{{15x+5y=1200}}} Multiply.




So we have the given system of equations:


{{{system(5x+25y=1100,15x+5y=1200)}}}



{{{-5(15x+5y)=-5(1200)}}} Multiply the both sides of the second equation by -5.



{{{-75x-25y=-6000}}} Distribute and multiply.



So we have the new system of equations:


{{{system(5x+25y=1100,-75x-25y=-6000)}}}



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+25y)+(-75x-25y)=(1100)+(-6000)}}}



{{{(5x-75x)+(25y-25y)=1100+-6000}}} Group like terms.



{{{-70x+0y=-4900}}} Combine like terms.



{{{-70x=-4900}}} Simplify.



{{{x=(-4900)/(-70)}}} Divide both sides by {{{-70}}} to isolate {{{x}}}.



{{{x=70}}} Reduce.



------------------------------------------------------------------



{{{5x+25y=1100}}} Now go back to the first equation.



{{{5(70)+25y=1100}}} Plug in {{{x=70}}}.



{{{350+25y=1100}}} Multiply.



{{{25y=1100-350}}} Subtract {{{350}}} from both sides.



{{{25y=750}}} Combine like terms on the right side.



{{{y=(750)/(25)}}} Divide both sides by {{{25}}} to isolate {{{y}}}.



{{{y=30}}} Reduce.



So the solutions are {{{x=70}}} and {{{y=30}}}.



Which form the ordered pair *[Tex \LARGE \left(70,30\right)].



This means that the system is consistent and independent.