## Answers

Start with the given system of equations: {{{system(5x+2y=-13,7x-3y=17)}}} {{{3(5x+2y)=3(-13)}}} Multiply the both sides of the first equation by 3. {{{15x+6y=-39}}} Distribute and multiply. {{{2(7x-3y)=2(17)}}} Multiply the both sides of the second equation by 2. {{{14x-6y=34}}} Distribute and multiply. So we have the new system of equations: {{{system(15x+6y=-39,14x-6y=34)}}} Now add the equations together.

You can do this by simply adding the two left sides and the two right sides separately like this: {{{(15x+6y)+(14x-6y)=(-39)+(34)}}} {{{(15x+14x)+(6y-6y)=-39+34}}} Group like terms. {{{29x+0y=-5}}} Combine like terms. {{{29x=-5}}} Simplify. {{{x=(-5)/(29)}}} Divide both sides by {{{29}}} to isolate {{{x}}}. ------------------------------------------------------------------ {{{15x+6y=-39}}} Now go back to the first equation.

{{{15(-5/29)+6y=-39}}} Plug in {{{x=-5/29}}}. {{{-75/29+6y=-39}}} Multiply. {{{cross(29)(-75/cross(29))+29(6y)=29(-39)}}} Multiply EVERY term by the LCD {{{29}}} to clear any fractions. {{{-75+174y=-1131}}} Multiply and simplify. {{{174y=-1131+75}}} Add {{{75}}} to both sides.

{{{174y=-1056}}} Combine like terms on the right side. {{{y=(-1056)/(174)}}} Divide both sides by {{{174}}} to isolate {{{y}}}. {{{y=-176/29}}} Reduce. So the solutions are {{{x=-5/29}}} and {{{y=-176/29}}}. Which form the ordered pair *[Tex LARGE left(-frac{5}{29},-frac{176}{29}right)].

This means that the system is consistent and independent..