The equation 6x-7y=5 has a unique solution if x, y are:
1) Real numbers
2) Rational numbers
3) Irrational numbers
4) Natural numbers
1. Real Numbers.
The equation 6x - 7y = 5 is a linear equation in two variables, x and y. To determine under which conditions the equation has a unique solution, we need to analyze the coefficient values and the type of numbers for x and y.
1) Real numbers: If x and y can be any real numbers, then the equation will always have a unique solution. This is because real numbers include all possible values, positive or negative, whole numbers or decimals.
2) Rational numbers: If x and y are restricted to rational numbers, which are numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero, the equation may or may not have a unique solution. It depends on whether or not the solution satisfies the equation.
3) Irrational numbers: If x and y are restricted to irrational numbers, which are numbers that cannot be expressed as a fraction, such as the square root of 2 or pi, the equation may or may not have a unique solution. Again, it depends on whether or not the solution satisfies the equation.
4) Natural numbers: If x and y are restricted to natural numbers, which are positive integers starting from 1, the equation may or may not have a unique solution. However, since the equation involves both x and y as variables, it is unlikely that there will be a unique solution using only natural numbers since there are infinite possibilities for both variables.
In summary, the equation 6x - 7y = 5 has a unique solution if x and y are any real numbers. For the other cases, whether the equation has a unique solution would depend on the specific values of x and y within the given restriction.