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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