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.