Question 143738
{{{x+3y-z=-2}}} Equation 1

{{{4x+6y+3z=4}}} Equation 2

{{{2x-y+2z=10}}} Equation 3




{{{2(x+3y-z)=2(-2)}}} Multiply both sides of Equation 1 by 2



{{{2x+6y-2z=-4}}} Distribute and multiply. Let's call this Equation 4



Now add Equation 4 to Equation 3 and call the result Equation 5


{{{2x+6y-2z=-4}}} Equation 4
+{{{2x-y+2z=10}}} Equation 3
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{{{4x+5y=6}}}     Equation 5






{{{3(x+3y-z)=3(-2)}}} Multiply both sides of Equation 1 by 3



{{{3x+9y-3z=-6}}} Distribute and multiply. Let's call this Equation 6



Now add Equation 5 to Equation 2  and call the result Equation 7


{{{3x+9y-3z=-6}}} Equation 5
+{{{4x+6y+3z=4}}} Equation 2
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{{{7x+15y=-2}}}   Equation 7




So we now have the two equations Equation 5 and Equation 7



{{{4x+5y=6}}}     Equation 5
{{{7x+15y=-2}}}   Equation 7



{{{-3(4x+5y)=-3(6)}}}     Multiply both sides of Equation 5 by -3
{{{7x+15y=-2}}}   Equation 7




{{{-12x-15y=-18}}}     Distribute
{{{7x+15y=-2}}}   Equation 7




Now add the equations


{{{-12x-15y=-18}}}   
+{{{7x+15y=-2}}}   
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{{{-5x=-20}}}



{{{x=(-20)/(-5)}}} Divide both sides of the resulting equation by -5 to isolate x



{{{x=4}}} Reduce. So this is the first part of our answer.



{{{7x+15y=-2}}}   Go back to Equation 7



{{{7(4)+15y=-2}}}   Plug in {{{x=4}}}



{{{28+15y=-2}}}   Multiply 



{{{15y=-2-28}}}Subtract 28 from both sides



{{{15y=-30}}} Combine like terms on the right side



{{{y=(-30)/(15)}}} Divide both sides by 15 to isolate y




{{{y=-2}}}  Reduce. So this is the second part of our answer.




{{{x+3y-z=-2}}} Go back to Equation 1



{{{4+3(-2)-z=-2}}} Plug in {{{x=4}}} and {{{y=-2}}} 



{{{4-6-z=-2}}} Multiply 




{{{-z-2=-2}}} Combine like terms on the left side



{{{-z=-2+2}}}Add 2 to both sides



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



{{{z=(0)/(-1)}}} Divide both sides by -1 to isolate z




{{{z=0}}} Divide. So this is the third part of our answer.


 

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Answer:


So our answer is 


{{{x=4}}},{{{y=-2}}} and {{{z=0}}}



which forms the point (4,-2,0)