Answer:
Step-by-step explanation:
To find the values of x, y, and z that satisfy the given system of equations:
1. Begin by writing down the equations:
2x + 2z = 4
5x + 3y = 17
3y − 4z = 11
(x, y, z) =
2. We can simplify the first equation by dividing both sides by 2:
x+z=2
3. Next, isolate y in the second equation by subtracting 5x from both sides:
3y=17-5x
4. Then, divide by 3 to find the value of y:
y=17/3-5x/3
5. Now, substitute the expression for y into the third equation:
y=17/3-5x/3-4z=11
6. Simplify the equation:
17-5x-4z=11
7. Rearrange terms to isolate z:
-5x-4z=11-17
8. Now, we have the equations x + z = 2 and 5x + 4z = 6. Solve this system of equations to find the values of x and z.
9. Once you have found the values of x and z, substitute them back into one of the original equations to solve for y.
10. Your final solution in the form of (x, y, z) will give you the values that satisfy all three equations simultaneously.