Question

SystemEquations: solve x and y

Solve x – 2y – 3z = 3
3x + y + z = 12
3x – 2y – 4z = 15

Answer 1

Answers: (0, 0, -1)

(3, 12, 15)

(3, 9, -6)

(-3, -9, 6)

Answer 2

[1], [2], [3], etc. denote whether it is the first, second or third equation, etc.
\[\large x – 2y – 3z = 3[1]\]
\[\large 3x + y + z = 12[2]\]
\[\large 3x – 2y – 4z = 15[3]\]
\[[1]\times 3\]
\[\large 3(x – 2y – 3z)=3(3)\]
\[\large 3x-6y-9z=9[4]\]
\[[2]-[3]\]
\[\large (3x + y + z)-(3x – 2y – 4z)=(12)-(15)\]
\[\large y+2y+z+4z=-3\]
\[\large 3y+5z=-3[5]\]
\[[2]-[4]\]
\[\large (3x + y + z)-(3x-6y-9z)=(12)-(9)\]
\[\large y+6y+z+9z=3\]
\[\large 7y+10z=3[6]\]
\[[5]\times 2\]
\[\large 2(3y+5z)=2(-3)\]
\[\large 6y+10z=-6[7]\]
\[[6]-[7]\]
\[\large (7y+10z)-(6y+10z)=(3)-(-6)\]
\[\large 7y-6y=3+6\]
\[\large y=9\]
Sub the y-value into either equation [6] or [7] to find z.
\[\large 7y+10z=3[6]\]
\[\large 7(9)+10z=3\]
\[\large 10z=3-63\]
\[\large 10z=-60\]
\[\large z=-6\]
To find x, sub in the y and z values into either equation [1], [2], [3] or [4].

Answer 3

gaussian elimination

Answer 4

Thanks Man!

Answer 5

But you don't need to find x to know which option is the correct one to choose from.

Answer 6

Agreed

Answer 7

do you know you understand how to get the answer ...?

Answer 8

Yes

Answer 9

:)