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ziro4ka [17]
3 years ago
13

Solve the systems of equations 2x+2y+6z=8 5x+6y+5z =3 5x+6y+3z=3

Mathematics
1 answer:
vlabodo [156]3 years ago
4 0

Answer:

x=21\\y=-17\\z=0

Step-by-step explanation:

Multiply the second equation by -1:

(-1)5x+6y+5z=3(-1)\\-5x-6y-5z=-3

Add this equation and the third equation and solve for "z":

\left \{ {{-5x-6y-5z=-3} \atop {5x+6y+3z=3}} \right.\\.........................\\-2z=0\\z=0

Substitute z=0 into two original equations:

2x+2y+6(0)=8

2x+2y=8        [Equation A]

5x+6y+5(0)=3  

5x+6y=3       [Equation B]

Multiply the Equation A by -3, add both equations and then solve for "x":

\left \{ {{-6x-6y=-24} \atop {5x+6y=3}} \right.\\.....................\\-x=-21\\x=21

Substitute x=21 into the Equation A or the Equation B and solve for "y":

2(21)+2y=8\\\\42+2y=8\\\\2y=8-42\\\\2y=-34\\\\y=\frac{-34}{2}\\\\y=-17

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