Question 127298


Start with the given system of equations:


{{{system(3x-y=4,-9x+3y=-12)}}}




Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.





So let's isolate y in the first equation


{{{3x-y=4}}} Start with the first equation



{{{-y=4-3x}}}  Subtract {{{3x}}} from both sides



{{{-y=-3x+4}}} Rearrange the equation



{{{y=(-3x+4)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=((-3)/(-1))x+(4)/(-1)}}} Break up the fraction



{{{y=3x-4}}} Reduce




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Since {{{y=3x-4}}}, we can now replace each {{{y}}} in the second equation with {{{3x-4}}} to solve for {{{x}}}




{{{-9x+3highlight((3x-4))=-12}}} Plug in {{{y=3x-4}}} into the first equation. In other words, replace each {{{y}}} with {{{3x-4}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{-9x+(3)(3)x+(3)(-4)=-12}}} Distribute {{{3}}} to {{{3x-4}}}



{{{-9x+9x-12=-12}}} Multiply



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



{{{0=-12+12}}}Add 12 to both sides



{{{0=0}}} Combine like terms on the right side





Since this equation is always true for any x value, this means x can equal any number. So there are an infinite number of solutions.