Question 202424

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

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

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{{{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.

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{{{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.