Question

How many solutions does the equation 3x - 7y=12 has?

Answer 1

The equation 3x - 7y = 12 has infinitely many solutions.

• An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.
• Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
• An equation which takes up the form $Ax+By+C=0$ where all of A, B and C are real numbers with A and B being non-zero real numbers. Now, it is convenient to find the number of solutions that an equation can have, by citing comparison with the given equation.

Now, the given equation is, 3x - 7y = 12.

Now, taking the standard equation and the given equation in question, we get,

$\frac{A}{3} \neq \frac{B}{-7}$

This gives the conclusion that our given equation has infinitely many solutions.

Hence, the equation 3x - 7y = 12 has infinitely many solutions.

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