Solve the system of three equations in three variables by an appropriate method.
5x + 2z = 3y - 24
3x = 5 + 4z
15 - 10z = 7y
Which three-dimensional point in the form (x, y, z) could be represented by the solution of system of three equations in three variables?
(-13.04, -6.78, 18.26)
B
（-1,5，-2）
(-4.11, -4.04, 4.33)
D
(-2.32, 02.13, -2.99)
To solve the system of three equations in three variables, we can use the method of substitution.
First, let's solve equation 2 for x:
3x = 5 + 4z
x = (5 + 4z)/3
Now, substitute this value of x into equations 1 and 3:
5((5 + 4z)/3) + 2z = 3y - 24
15 + 20z + 6z = 9y - 72
26z + 15 = 9y - 72
26z = 9y - 87
15 - 10z = 7y
Now we have a system of two equations with two variables (y and z):
26z = 9y - 87
15 - 10z = 7y
Let's solve the second equation for y:
15 - 10z = 7y
7y = -10z + 15
y = (-10z + 15)/7
Now, substitute this value of y into the first equation:
26z = 9((-10z + 15)/7) - 87
26z = (-90z + 135)/7 - 87
26z = (-90z + 135 - 609)/7
26z = (-90z - 474)/7
182z = -90z - 474
272z = -474
z = -474/272
z = -1.75
Now, substitute this value of z back into the equation y = (-10z + 15)/7 to solve for y:
y = (-10(-1.75) + 15)/7
y = (17.5 + 15)/7
y = 32.5/7
y ≈ 4.64
Now, substitute the values of y and z into the equation x = (5 + 4z)/3 to solve for x:
x = (5 + 4(-1.75))/3
x = (5 - 7)/3
x = -2/3
x ≈ -0.67
Therefore, the solution to the system of three equations in three variables is approximately (-0.67, 4.64, -1.75).
None of the given answer choices match this solution.