Either an infinite number or none.
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A linear equation is that of a straight line. Any one of the infinitely many points on the line will be solutions. If the equation is in terms of the variables x and y, just pick any two values of x, solve for y and the results will be the coordinates of two solutions.
No. A pair of linear equation can have 0 solutions (they are parallel), or one solution (they cross at one point) or an infinite number of solutions (they represent the same line).
A linear equation.
the Bratu's equation is a differential equation which is non-linear (such as, if we have some solutions for it, a linear combinaison of these solutions will not be everytime a solution). It's given by the equation y''+a*e^y=0 or d²y/dy² =-ae^y.
It is a quadratic equation that normally has two solutions