Question 198335
{{{9x+4y=-32}}} Start with the first equation.



{{{9(1-5y)+4y=-32}}}  Plug in {{{x=1-5y}}} into the first equation. In other words, replace each {{{x}}} with {{{1-5y}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{9-45y+4y=-32}}} Distribute



{{{-41y+9=-32}}} Combine like terms on the left side



{{{-41y=-32-9}}}Subtract 9 from both sides



{{{-41y=-41}}} Combine like terms on the right side



{{{y=(-41)/(-41)}}} Divide both sides by -41 to isolate y




{{{y=1}}} Divide





Now that we know that {{{y=1}}}, we can plug this into {{{x=1-5y}}} to find {{{x}}}



{{{x=1-5y}}} Start with the second equation



{{{x=1-5(1)}}} Plug in {{{y=1}}}



{{{x=1-5}}} Multiply



{{{x=-4}}} Subtract



So our answers are {{{x=-4}}} and {{{y=1}}} which form the ordered pair *[Tex \LARGE \left(-4,1\right)]




Notice if we graph the two equations, we can see that their intersection is at *[Tex \LARGE \left(-4,1\right)]. So this verifies our answer.



{{{ graph( 500, 500, -5, 5, -5, 5, (-32-9x)/4, (x-1)/(-5)) }}} Graph of {{{9x+4y=-32}}} (red) and {{{x=1-5y}}} (green)