Solve the following simultaneous equations: x + y + z = 4 2x - 3y + 4z = 33

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x - 3y + 4(4 - x - y) = 33
2x - 3y + 16 - 4x - 4y = 33
-2x - 7y = 17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x + 7y = -17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x + 7y = -17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x + 7y = -17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x + 7y = -17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x + 7y = -17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x + 7y = -17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x + 7y = -17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x + 7y = -17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x + 7y = -17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms of x and y:
z = 4 - x - y

Now, substitute this expression for z into the second equation:
2x + 7y = -17
2x + 7y = -17

Now, we have a new system of equations:
x + y + z = 4
2x + 7y = -17

From the first equation, we can express z in terms

$$x \ \ y \ \ z =4$$

$$2x-3y \ 4z =33$$

$$x=4-y-z$$

$$2(4-y-z)-3y \ 4z =33$$

$$8-2y-2z-3y \ 4z =33$$

$$5y+6z=25$$

$$5y=25-6z$$

$$y=(5-6z)/5$$

$$x=4-(5-6z)/5-z$$

$$x=(4\times5-5+6z)/5-z$$

$$x=(20-6z)/5-z$$

$$=(20-6z-5z)/5$$

$$x=(20-11z)/5$$

$$z=3 \ \ y=3/5 \ \ x=3$$