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

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

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7 hours, 0 minutes, 0 seconds

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0.04

total weeks

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0.29

total days

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7.00

total hours

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420.00

total minutes

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25,200.00

total seconds

step-by-step explanation: