Question 202422
{{{0.3x-0.2y=4}}} Start with the first equation.



{{{10(0.3x)-10(0.2y)=10(4)}}} Multiply EVERY term by 10 to make every number a whole number.



{{{3x-2y=40}}} Multiply


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{{{0.5x+0.3y=1}}} Move onto the second equation.



{{{10(0.5x)+10(0.3y)=10(1)}}} Multiply EVERY term by 10 to make every number a whole number.



{{{5x+3y=10}}} Multiply




So we have the given system of equations:


{{{system(3x-2y=40,5x+3y=10)}}}



{{{3(3x-2y)=3(40)}}} Multiply the both sides of the first equation by 3.



{{{9x-6y=120}}} Distribute and multiply.



{{{2(5x+3y)=2(10)}}} Multiply the both sides of the second equation by 2.



{{{10x+6y=20}}} Distribute and multiply.



So we have the new system of equations:


{{{system(9x-6y=120,10x+6y=20)}}}



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



{{{(9x-6y)+(10x+6y)=(120)+(20)}}}



{{{(9x+10x)+(-6y+6y)=120+20}}} Group like terms.



{{{19x+0y=140}}} Combine like terms.



{{{19x=140}}} Simplify.



{{{x=(140)/(19)}}} Divide both sides by {{{19}}} to isolate {{{x}}}.



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{{{9x-6y=120}}} Now go back to the first equation.



{{{9(140/19)-6y=120}}} Plug in {{{x=140/19}}}.



{{{1260/19-6y=120}}} Multiply.



{{{cross(19)(1260/cross(19))-19(6y)=19(120)}}} Multiply both sides by the LCD {{{19}}} to clear any fractions.



{{{1260-114y=2280}}} Distribute and multiply.



{{{-114y=2280-1260}}} Subtract {{{1260}}} from both sides.



{{{-114y=1020}}} Combine like terms on the right side.



{{{y=(1020)/(-114)}}} Divide both sides by {{{-114}}} to isolate {{{y}}}.



{{{y=-170/19}}} Reduce.



So the solutions are {{{x=140/19}}} and {{{y=-170/19}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{140}{19},-\frac{170}{19}\right)].



This means that the system is consistent and independent.



Note: the approximate solutions are {{{x=7.368}}} and {{{y=-8.947}}}