Use the elimination method or substitution method to tell whether the Linear System has infinitely many solutions, one solution, or no solution.

x-4y=2
2x-8y=5

Question

Use the elimination method or substitution method to tell whether the Linear System has infinitely many solutions, one solution, or no solution.

x-4y=2 
2x-8y=5

mathstudent55 · Answer

The second equation has 2x. The first equation has x.
If you multiply the first equation by -2, you will have -2x, and the x terms will be eliminated.

Multiply the first equation by -2.
Now add the new equation to the second equation.
What do you get?
If you get an equation in y, there is one solution.
If you get a true statement with no variables, there is an infinite number of solutions.
If you get a false statement, there is no solution.