Question

Find a value of M that will give you a system of equations with exactly one solution.

Answer 1

Given:

System of equations is

$y=6x+1$

$y=mx+1$

To find:

A value of M that will give you a system of equations with exactly one solution.

Solution:

A system of equation has exactly one solution if the graph of the equation is neither parallel nor coincident.

Slope of parallel lines are same. But in the given equations if slopes are same then both the system of equations have two same equations which represent coincident lines.

For one solution, $m\neq 6$.

So, the value of m can be any real number except 6 because for m=6.

Thus, $m=R-{6}$.

1 is a real number which is not equal to 6.

Therefore, one possible value of m is 1.