Question 178292
{{{5x+2y=-36}}} Start with the first equation.



{{{5(6-7y)+2y=-36}}}  Plug in {{{x=6-7y}}}. In other words, replace each {{{x}}} with {{{6-7y}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{30-35y+2y=-36}}} Distribute



{{{-33y+30=-36}}} Combine like terms on the left side



{{{-33y=-36-30}}}Subtract 30 from both sides



{{{-33y=-66}}} Combine like terms on the right side



{{{y=(-66)/(-33)}}} Divide both sides by -33 to isolate y




{{{y=2}}} Divide





Now that we know that {{{y=2}}}, we can plug this into {{{x=6-7y}}} to find {{{x}}}



{{{x=6-7y}}} Move onto the second equation.



{{{x=6-7(2)}}} Plug in {{{y=2}}}



{{{x=6-14}}} Multiply



{{{x=6-14}}} Combine like terms.



So our answer is {{{x=-8}}} and {{{y=2}}} which form the ordered pair *[Tex \LARGE \left(-8,2\right)]




Notice if we graph the two equations, we can see that their intersection is at *[Tex \LARGE \left(-8,2\right)]. So this verifies our answer.



{{{drawing(500, 500, -10, 10, -10, 10, 
grid(1),
graph( 500, 500, -10, 10, -10, 10, (-36-5x)/2, (x-6)/(-7)),
circle(-8,2,0.05),
circle(-8,2,0.08),
circle(-8,2,0.11)
) }}} Graph of {{{5x+2y=-36}}} (red) and {{{x=6-7y}}} (green)