Question

This system of equations has an infinite number of solutions. Define the solutions algebraically, and allow z to represent all real numbers.
3x − 4y + 4z = 7
x − y − 2z = 2
2x − 3y + 6z = 5
x =

y =

z = all real numbers

Answer 1

Answer:

x = 12z + 1  and y = 10z - 1

Step-by-step explanation:

To solve the system of equations, we can use the substitution method

If we call

3x - 4y + 4z = 7 I

x - y - 2z = 2 II

2x - 3y + 6z = 5 III

Clearing II  x = 2 + y + 2z

Now, replacing II in III

2(2 + y + 2z) - 3y +6z = 5

4 + 2y + 4z - 3y + 6z = 5

10z - y = 1 from here y = 10z - 1

Finally, replacing y in I

3x - 4(10z - 1) + 4z = 7

3x -40z + 4 + 4z = 7

3x - 36z = 3

3x = 36z + 3

x = 12z + 1

Done