Question

Solve the system of equations:

X + y + z &= 2
Ex - y - 5z &= -36
-X - Y - 8Z &= -30

a) X = 5, y = 1, z = -4
b) X = -3, y = 4, z = 1
c) X = 2, y = 3, z = -1
d) X = -1, y = -2, z = 5

Answer 1

To solve the given system of equations, we can use the method of substitution. By substituting the values of x, y, and z from the given answer choices into the equation, we can determine the correct solution. The correct answer is d) X = -1, y = -2, z = 5.

Step-by-step explanation:

To solve the system of equations:

X + y + z = 2

Ex - y - 5z = -36

-X - Y - 8Z = -30

First, we can add the second and third equations to eliminate the y variable:

Ex - y - 5z + (-X - Y - 8Z) = -36 + (-30)

E - X - Y - y - Y = -66

(E - 1) X - (1 + 2Y) = -66

Next, we substitute the value of x from the first equation into this equation:

(E - 1)(2 - y - z) - (1 + 2Y) = -66

Simplifying, we get: (E - 1)(-y - z) - (1 + 2Y) = -66

Next, we substitute the values of y and z from the first equation into this equation:

(E - 1)(-1 - z) - (1 + 2(2 - x - z)) = -66

Expanding and combining like terms, we get: (E - 1)(-1 - z) - (1 + 4 - 2x - 2z) = -66

(1 - E)(1 + z) = -1 - 2 + 2x + 2z - 66

(1 - E)(1 + z) = 2x + 2z - 67

Now, we can substitute the values of x, y, and z from the given answer choices into this equation to find the correct solution. Only option d) X = -1, y = -2, and z = 5 satisfies this equation.

Therefore, the correct answer is d) X = -1, y = -2, z = 5.