Question 131039
Start with the given system

{{{y=6x+8}}}
{{{y=9x+10}}}




{{{9x+10=6x+8}}}  Plug in {{{y=9x+10}}} into the first equation. In other words, replace each {{{y}}} with {{{9x+10}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.





{{{9x=6x+8-10}}} Subtract 10 from both sides



{{{9x-6x=8-10}}} Subtract 6x from both sides



{{{3x=8-10}}} Combine like terms on the left side



{{{3x=-2}}} Combine like terms on the right side



{{{x=(-2)/(3)}}} Divide both sides by 3 to isolate x







Now that we know that {{{x=-2/3}}}, we can plug this into {{{y=9x+10}}} to find {{{y}}}




{{{y=9(-2/3)+10}}} Substitute {{{-2/3}}} for each {{{x}}}



{{{y=4}}} Simplify



So our answer is {{{x=-2/3}}} and {{{y=4}}} which also looks like *[Tex \LARGE \left(-\frac{2}{3},4\right)]




Notice if we graph the two equations, we can see that their intersection is at *[Tex \LARGE \left(-\frac{2}{3},4\right)]. So this verifies our answer.



{{{ graph( 500, 500, -5, 5, -5, 5, 6x+8, 9x+10) }}} Graph of {{{y=6x+8}}} (red) and {{{y=9x+10}}} (green)