Question 202424
{{{4x-9y=10.5}}} Start with the first equation.



{{{10(4x)-10(9y)=10(10.5)}}} Multiply EVERY term by 10 to make every value a whole number.



{{{40x-90y=105}}} Multiply.



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


{{{7y-2x=-6.5}}} Move onto the second equation.



{{{-2x+7y=-6.5}}} Rearrange the terms.



{{{10(-2x)+10(7y)=10(-6.5)}}} Multiply EVERY term by 10 to make every value a whole number.



{{{-20x+70y=-65}}} Multiply.




So we have the given system of equations:


{{{system(40x-90y=105,-20x+70y=-65)}}}



{{{2(-20x+70y)=2(-65)}}} Multiply the both sides of the second equation by 2.



{{{-40x+140y=-130}}} Distribute and multiply.



So we have the new system of equations:


{{{system(40x-90y=105,-40x+140y=-130)}}}



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



{{{(40x-90y)+(-40x+140y)=(105)+(-130)}}}



{{{(40x-40x)+(-90y+140y)=105+-130}}} Group like terms.



{{{0x+50y=-25}}} Combine like terms.



{{{50y=-25}}} Simplify.



{{{y=(-25)/(50)}}} Divide both sides by {{{50}}} to isolate {{{y}}}.



{{{y=-1/2}}} Reduce.



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



{{{40x-90y=105}}} Now go back to the first equation.



{{{40x-90(-1/2)=105}}} Plug in {{{y=-1/2}}}.



{{{40x+45=105}}} Multiply.



{{{40x=105-45}}} Subtract {{{45}}} from both sides.



{{{40x=60}}} Combine like terms on the right side.



{{{x=(60)/(40)}}} Divide both sides by {{{40}}} to isolate {{{x}}}.



{{{x=3/2}}} Reduce.



So the solutions are {{{x=3/2}}} and {{{y=-1/2}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{3}{2},-\frac{1}{2}\right)].



This means that the system is consistent and independent.