Question 124877
Start with the given system

{{{-6x+8y=36}}}
{{{y=4x+11}}}




{{{-6x+8(4x+11)=36}}}  Plug in {{{y=4x+11}}} into the first equation. In other words, replace each {{{y}}} with {{{4x+11}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{-6x+32x+88=36}}} Distribute



{{{26x+88=36}}} Combine like terms on the left side



{{{26x=36-88}}}Subtract 88 from both sides



{{{26x=-52}}} Combine like terms on the right side



{{{x=(-52)/(26)}}} Divide both sides by 26 to isolate x




{{{x=-2}}} Divide





Now that we know that {{{x=-2}}}, we can plug this into {{{y=4x+11}}} to find {{{y}}}




{{{y=4(-2)+11}}} Substitute {{{-2}}} for each {{{x}}}



{{{y=3}}} Simplify



So our answer is {{{x=-2}}} and {{{y=3}}} which also looks like *[Tex \LARGE \left(-2,3\right)]




Notice if we graph the two equations, we can see that their intersection is at *[Tex \LARGE \left(-2,3\right)]. So this verifies our answer.



{{{ graph( 500, 500, -5, 5, -5, 5, (36+6x)/8, 4x+11) }}} Graph of {{{-6x+8y=36}}} (red) and {{{y=4x+11}}} (green)