Question 146537
1)

------------------ Let's test the first equation ------------------

{{{2x-y+z=5}}} Start with the first equation.



{{{2*(5)-(-2)+(2)=5}}} Plug in {{{x=5}}}, {{{y=-2}}}, and {{{z=2}}}.



{{{14=5}}} Evaluate and simplify the left side.



Since the equation is <b>not</b> true, this means that (5, -2, 2) is <b>not</b> a solution to the system. Remember, a solution has to satisfy <b>all</b> of the equations in the system.




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2)

------------------ Let's test the first equation ------------------



{{{4x+2y+3z=11}}} Start with the first equation.



{{{4*(1)+2*(-1)+3*(3)=11}}} Plug in {{{x=1}}}, {{{y=-1}}}, and {{{z=3}}}.



{{{11=11}}} Evaluate and simplify the left side.


Notice how the equation is true.


------------------ Now let's test the second equation ------------------



{{{x-2y+z=6}}} Start with the second equation.



{{{(1)-2*(-1)+(3)=6}}} Plug in {{{x=1}}}, {{{y=-1}}}, and {{{z=3}}}.



{{{6=6}}} Evaluate and simplify the left side.


Notice how the equation is true.


------------------ Now let's test the third equation ------------------



{{{2x+y+2z=7}}} Start with the third equation.



{{{2*(1)+(-1)+2*(3)=7}}} Plug in {{{x=1}}}, {{{y=-1}}}, and {{{z=3}}}.



{{{7=7}}} Evaluate and simplify the left side.


Notice how the equation is true.





Since <b>all</b> of the equations in the system are true, this means that (1, -1, 3) is a solution.