To solve this system of equations, we can use the method of substitution or elimination.
Using elimination method:
2x + 4y - 6z = 28
2x + 3y + 2z = 92x + 4y - 6z = 28
7y - 4z = 37
7y - 4z = 373x + 4y + z = 16
21y - 12z = 1113x + 4y + z = 16
3x + 25y = 127
3x = 127 - 25yx = (127 - 25y) / 3
(127 - 25y) / 3 + 2y = 9(127 - 25y) + 6y = 27127 - 19y = 27-19y = -100y = 5.26
x = (127 - 25*5.26) / 3 = 2.69Substitute y = 5.26 and solve for x:
2.69 + 3*5.26 + 2z = 92.69 + 15.78 + 2z = 918.47 + 2z = 92z = -9.47z = -4.74
Therefore, the solution to the system of equations is:x = 2.69, y = 5.26, z = -4.74
To solve this system of equations, we can use the method of substitution or elimination.
Using elimination method:
Multiply the second equation by 2 to make the coefficient of x the same in the first and second equations:2x + 4y - 6z = 28
Add the first and modified second equation:2x + 3y + 2z = 9
2x + 4y - 6z = 28
7y - 4z = 37
Now, we have two equations:7y - 4z = 37
Multiply the first equation by 3 and add to the third equation:3x + 4y + z = 16
21y - 12z = 111
3x + 4y + z = 16
3x + 25y = 127
Rearrange this equation to solve for x:3x = 127 - 25y
Substitute this value of x back into one of the original equations, like the first one:x = (127 - 25y) / 3
(127 - 25y) / 3 + 2y = 9
Now that we have the value of y, substitute back into one of the equations to find the values of x and z:(127 - 25y) + 6y = 27
127 - 19y = 27
-19y = -100
y = 5.26
x = (127 - 25*5.26) / 3 = 2.69
Substitute y = 5.26 and solve for x:
2.69 + 3*5.26 + 2z = 9
2.69 + 15.78 + 2z = 9
18.47 + 2z = 9
2z = -9.47
z = -4.74
Therefore, the solution to the system of equations is:
x = 2.69, y = 5.26, z = -4.74