Explain why a system of three equations in three variables can have infinitely many solutions

we know that

we will get solution of three system of equations when intersects at one point

For example:

x+2y-3z=-3

2x-5y+4z=13

5x+4y-z=5

These three system of equations has one solutions

so, it has unique solution

that is (2, -1 , 1)

And when planes are lying on one another

then we can get infinite solutions

For example:

x+2y-3z=-3

2x+4y-6z=-6

5x+4y-z=5

So, we will get value of x and y in terms of z

and z can be any value

so, x and y can also be any values

that's why there would be infinite number of solutions

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step-by-step explanation:

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