Question 198719
{{{3x+4y=9}}} Start with the first equation.



{{{3x+4(x-3)=9}}}  Plug in {{{y=x-3}}} into the first equation. In other words, replace each {{{y}}} with {{{x-3}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{3x+4x-12=9}}} Distribute



{{{7x-12=9}}} Combine like terms on the left side



{{{7x=9+12}}}Add 12 to both sides



{{{7x=21}}} Combine like terms on the right side



{{{x=(21)/(7)}}} Divide both sides by 7 to isolate x



{{{x=3}}} Divide



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



{{{y=x-3}}} Start with the second equation.



{{{y=(3)-3}}} Plug in {{{x=3}}}



{{{y=0}}} Subtract



So our solutions are {{{x=3}}} and {{{y=0}}} which form the ordered pair *[Tex \LARGE \left(3,0\right)]




Notice if we graph the two equations, we can see that their intersection is at *[Tex \LARGE \left(3,0\right)]. So this verifies our answer.



{{{ graph( 500, 500, -5, 5, -5, 5, (9-3x)/4, x-3) }}} Graph of {{{3x+4y=9}}} (red) and {{{y=x-3}}} (green)