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Yes and sometimes it can have more than one solution.
Yes and yes. eg x = y + 1 has an infinite number of solutions, and {sin(x) + cos(x) = 2} does not have a solution.
-- If the equation has only one variable (like 'x' or 'y'), and the only power of the variable anywhere in the equation is '1', then the equation has one solution. -- If the variable appears raised to powers higher than '1', then there are as many solutions as the highest power of the variable. -- If the equation has two or more variables, then there are an infinite number of solutions.
It's the equation of a straight-line graph. Every point on the line is a solution of the equation. There are an infinite number of them.
A single equation in two variables is, for example. Its graph is a line, and every point on the line is a solution.