Question

Solve the system of equation

Answer 1

x = 0

y = 1

z = -4

Explanation:

6x + 4y + 1z = 0 => z = -6x -4y

If 12x - 4y - 5z = 16, then

12x - 4y - 5(-6x - 4y) = 16

12x - 4y + 30x + 20y = 16

42x + 16y = 16 => 21x + 8y = 8

then y = (8 - 21x)/8

if -24x - 4y + 5z = -24

-24x - 4y + 5(-6x -4y) = -24

-24x - 4y - 30x - 20y = -24

-54x - 24y = -24 => -9x - 4y = -4

substitute y = (8 - 21x)/8

then -9x - 4(8 -21x)/8 = -4

-9x - 1/2(8 -21x) = -4

times 2 in both side

-18x - (8 - 21x) = -8

-18x - 8 + 21x = -8

3x = -8 + 8

3x = 0

x = 0

then y = (8 - 21x)/8 = (8 - 21(0))/8 = (8 - 0)/8 = 8/8 = 1

then z = -6x -4y = -6(0) - 4(1) = 0 - 4 = -4

Hope this helps