To solve this system of equations, we can use the method of substitution or elimination.
Let's start by rearranging the equations:
From equation 1, we can express x in terms of y and z:x = 13 - 2y - 3z
Now substitute x into equations 2 and 3:
3(13 - 2y - 3z) + 2y + 2z = 1639 - 6y - 9z + 2y + 2z = 16-4y - 7z = -23
4(13 - 2y - 3z) - 2y + 5z = 552 - 8y - 12z - 2y + 5z = 5-10y - 7z = -47
Now we have a system of two equations in terms of y and z:
We can solve this system using either substitution or elimination method. Let's use the elimination method:
Multiplying equation 1 by -2 and adding it to equation 2:
-2y + 7z = -1
Now, we can solve for y in terms of z:
-2y = -7z + 1y = (7z - 1) / 2
Now we can substitute the value of y back into one of the initial equations to solve for z:
-4(7z - 1) / 2 - 7z = -23-14z + 2 - 7z = -23-21z = -25z = 25 / 21z = 1.19
Finally, substitute the values of y and z back into one of the initial equations to solve for x:
x = 13 - 2(7/2 - 1) - 3(1.19)x = 13 - 7 - 3.57x = 2.43
Therefore, the solution to the system of equations is:x = 2.43y = 2.14z = 1.19
To solve this system of equations, we can use the method of substitution or elimination.
Let's start by rearranging the equations:
x + 2y + 3z = 133x + 2y + 2z = 164x - 2y + 5z = 5From equation 1, we can express x in terms of y and z:
x = 13 - 2y - 3z
Now substitute x into equations 2 and 3:
3(13 - 2y - 3z) + 2y + 2z = 16
39 - 6y - 9z + 2y + 2z = 16
-4y - 7z = -23
4(13 - 2y - 3z) - 2y + 5z = 5
52 - 8y - 12z - 2y + 5z = 5
-10y - 7z = -47
Now we have a system of two equations in terms of y and z:
-4y - 7z = -23-10y - 7z = -47We can solve this system using either substitution or elimination method. Let's use the elimination method:
Multiplying equation 1 by -2 and adding it to equation 2:
8y + 14z = 46-10y - 7z = -47
-2y + 7z = -1
Now, we can solve for y in terms of z:
-2y = -7z + 1
y = (7z - 1) / 2
Now we can substitute the value of y back into one of the initial equations to solve for z:
-4(7z - 1) / 2 - 7z = -23
-14z + 2 - 7z = -23
-21z = -25
z = 25 / 21
z = 1.19
Finally, substitute the values of y and z back into one of the initial equations to solve for x:
x = 13 - 2(7/2 - 1) - 3(1.19)
x = 13 - 7 - 3.57
x = 2.43
Therefore, the solution to the system of equations is:
x = 2.43
y = 2.14
z = 1.19