For the given set of equations:x+y = 1y+ z = 1x + z = 1,which one of the following statements is correct?a)Equations are inconsistent.b)Equations are consistent and a single non-trivial solution exists.c)Equations are consistent and many solutions exist.d)Equations are consistent and only a trivial solution exists.Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Explanation:

The given set of equations is:

xy = 1

yz = 1

xz = 1

To solve this system of equations, we can use the method of substitution. Let's first solve the first equation for y:

y = 1/x

We can substitute this value of y in the second equation:

z(1/x) = 1

Solving for z:

z = x

Now we can substitute both values of y and z in the third equation:

x(x) = 1

Solving for x:

x = 1

Now we can substitute this value of x in the first equation to find y:

y = 1/x = 1/1 = 1

Therefore, the solution to the system of equations is:

x = 1, y = 1, z = 1

This is a single non-trivial solution, which means that option (b) is correct.

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