Question

Solve the system of equations below:

9r + 3y - 4z = 37
4r + 3y + z = 16
x - 5y + 8z = -31.

Answer 1

To solve the system of equations, use the method of elimination. Multiply the equations to eliminate variables and then add the equations to find the values of 'r', 'y', and 'z'. The solution is r ≈ 1.29, y ≈ 2.61, and z ≈ -4.80.

Step-by-step explanation:

To solve the system of equations:

9r + 3y - 4z = 37

4r + 3y + z = 16

x - 5y + 8z = -31

1. We can use the method of elimination to solve this system.
2. First, let's eliminate the variable 'y' by multiplying the second equation by 3 and the third equation by -3.
3. The new system becomes:

9r + 3y - 4z = 37

12r + 9y + 3z = 48

-3x + 15y - 24z = 93

1. Next, let's eliminate the variable 'z' by multiplying the second equation by 4 and the third equation by -1.
2. The new system becomes:

9r + 3y - 4z = 37

16r + 12y + 4z = 64

3x - 15y + 24z = -93

1. Now, add the first equation to the second equation and add the second equation to the third equation.
2. You will obtain:

9r + 3y - 4z = 37

25r + 15y = 101

3x = -29

1. Finally, solve for 'x', 'y', and 'z' using the new equations.
2. You will find:

r ≈ 1.29

y ≈ 2.61

z ≈ -4.80