Question 166357
{{{-5x+4y+z=3}}} Start with the second equation



{{{z=3+5x-4y}}} Get every term but "z" to the right side


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{{{2x-3y+6z=-21}}} Move onto the first equation



{{{2x-3y+6(3+5x-4y)=-21}}} Plug in {{{z=3+5x-4y}}}



{{{2x-3y+18+30x-24y=-21}}} Distribute



{{{2x-3y+30x-24y=-21-18}}} Subtract 18 from both sides.



{{{32x-27y=-39}}} Combine like terms. So let's call this equation 4


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{{{7x-7y-4z=-6}}} Move onto the third equation



{{{7x-7y-4(3+5x-4y)=-6}}} Plug in {{{z=3+5x-4y}}}



{{{7x-7y-12-20x+16y=-6}}} Distribute



{{{7x-7y-20x+16y=-6+12}}} Add 12 to both sides



{{{-13x+9y=6}}} Combine like terms. So let's call this equation 5.



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So we now have the equations 


{{{32x-27y=-39}}} Equation 4
{{{-13x+9y=6}}}    Equation 5



Now let's solve the given system of equations 4 and 5



*[invoke solving_linear_system_by_substitution 32,-27,-39,-13,9,6]



{{{z=3+5x-4y}}} Go back to the first isolated equation



{{{z=3+5(3)-4(5)}}} Plug in {{{x=3}}} and {{{y=5}}}



{{{z=3+15-20}}} Multiply.



{{{z=-2}}} Combine like terms.



So the answer is {{{x=3}}}, {{{y=5}}}, and {{{z=-2}}} which forms the point (3,5,-2)