The number of X₁ + X2 + x3 + x4 + x5 + x6 = 12 in which ₂ = 3 non-negative integer solutions to the equation equals the number of non-negative integer solutions to the equation x₁ + x3 + x1 + x5 + x6 = 9. True False

What is Integer Solution:

A polynomial equation with at least two unknowns that has only integer solutions is known as a Diophantine equation. In a linear Diophantine equation, the sum of two or more degree one monomials acts as a constant. A Diophantine equation is referred to as exponential if the unknowns may be expressed as exponents. For diophantine problems, which have more unknowns than equations, it is necessary to find integers that concurrently solve all of the equations. These equational systems define algebraic surfaces, curves, and sets more generally.

Given:

Given statement is:

The number of non-negative integer solutions to the equation to the equation $x_1+x_2+x_3+x_4+x_5+x_6=12$ in which $x_2=3$ is equal to the number of non-negative integer solutions to the equation $x_1+x_3+x_4+x_5+x_6=9$.

To Determine:

We determine whether the given statement is true or false.