Question 218387
{{{2x+9y=-8}}} Start with the second equation.



{{{2x+9(-3x+13)=-8}}}  Plug in {{{y=-3x+13}}} into the second equation. In other words, replace each {{{y}}} with {{{-3x+13}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{2x+-27x+117=-8}}} Distribute



{{{-25x+117=-8}}} Combine like terms on the left side



{{{-25x=-8-117}}}Subtract 117 from both sides



{{{-25x=-125}}} Combine like terms on the right side



{{{x=(-125)/(-25)}}} Divide both sides by -25 to isolate x



{{{x=5}}} Divide



Now that we know that {{{x=5}}}, we can plug this into {{{y=-3x+13}}} to find {{{y}}}



{{{y=-3(5)+13}}} Substitute {{{5}}} for each {{{x}}}



{{{y=-2}}} Simplify



So our answer is {{{x=5}}} and {{{y=-2}}} which also looks like *[Tex \LARGE \left(5,-2\right)]




Notice if we graph the two equations, we can see that their intersection is at *[Tex \LARGE \left(5,-2\right)]. So this verifies our answer.



{{{ graph( 500, 500, -10, 10, -10, 10, -3x+13, (-8-2x)/9) }}} Graph of  and {{{y=-3x+13}}} (red) and {{{2x+9y=-8}}} (green)