Question

Find (if possible) conditions on a and b such that the following system has no solution, onesolution and infinitely many solutions.2 – 2y = 1ac + by = 5.

Answer 1

We are given the following system of equations

`\begin{gathered} x-2y=1 \\ ax+by=5 \end{gathered}`

Let us find the conditions on a and b such that the following system has no solution, one

solution and infinitely many solutions.

No solution:

A system of equations has no solution when the two equations are parallel.

Recall that two parallel equations have equal slopes.

If the value of a = 1 and the value of b = -2 then the two equations will be parallel and hence they will have no solution.

`\begin{gathered} x-2y=1 \\ x-2y=5 \end{gathered}`

The graph of the above system of equations is shown below