A 1 x b 1 y c 1 - 1 a 2 x b 2 y c 2 - 2 The given equations are consistent and dependent and have infinitely many solutions if and only if a 1 a 2 b 1 b 2 c 1 c 2 Conditions for Infinite Solution. Write an equation that has no solution. Subtracting 25 x from both sides 25 x 25 x 35 25 x 25 x 35 We have -35 -35 which is a True statement it will be true for any value of the variable x.
For example if the rref is has solution set 4-3z 52z z where z can be any real number.
Writing equations with a given number of solutions - Practice questions. Interval 1 32pi 32pi05. An equation can have infinitely many. When you end up with a true statement like this it means that the solution to the equation is all real numbers.