Question

11.) A system of two linear equations can have no solution, onesolution, or infinitely many solutions. Draw graphs or write aparagraph explaining how a graph of the two equations wouldappear for each of these possibilities,Ihp

Answer 1

The solution of a system of two linear equations interprets the point of intersection of the two lines geometrically

When the two lines intersect each other at a point, then the system of two linear equations has a unique solution.

If two linear equations in the given system represent two lines parallel to each other, then the system becomes inconsistent and in that case, it has no solution.

If the system is dependent i.e. there is only one linear equation in two variables, then every point on the line is the solution of the equation.

So, in that case, it has infinitely many solutions.