Final answer:
To solve the system of equations, we can use the method of substitution. By substituting the value of x into the other equations, we can find the values of y and z. The solution to the system of equations is (1/3, 2, 1.5) or approximately (0.33, 2, 1.5).
Step-by-step explanation:
To solve the system of equations:
3x + 2y + 4z = 11
2x - y + 3z = 4
5x - 3y + 5z = -1
We can use the method of elimination or substitution. Let's use the method of substitution.
- From equation 2, we can solve for x: x = (4 + y - 3z)/2.
- Substitute the value of x in equation 1 and equation 3.
After substituting, we get:
6 + 2y - 6z + 2y + 4z = 11
10 + 5y - 15z - 3y + 5z = -1
Simplify both equations:
4y - 2z = 5
2y - 10z = -11
Now, we have a system of two equations with two variables. We can solve this using either substitution or elimination.
Using elimination, multiply the first equation by 2 and the second equation by 4 to cancel out the y term:
8y - 4z = 10
8y - 40z = -44
Subtract the second equation from the first:
0 + 36z = 54
z = 1.5
Substitute the value of z into one of the equations to find y:
4y - 2(1.5) = 5
4y - 3 = 5
4y = 8
y = 2
Substitute the values of y and z into one of the original equations to find x:
3x + 2(2) + 4(1.5) = 11
3x + 4 + 6 = 11
3x = 1
x = 1/3
Therefore, the solution to the system of equations is (1/3, 2, 1.5) or approximately (0.33, 2, 1.5).