Question

Without graphing determine whether the system of linear equations has one solution infinitely many solutions or no solution explain your reasoning.

y=4x+8
y=5x+1

Answer 1

The answer for this is 9x=9

Answer 2

Infinitely many solutions.

Explanation:

First, make both equations equal to each other.

4x + 8 = 5x + 1

Subtract 4x from both sides.

8 = x + 1

Subtract 1 from both sides.

7 = x

When x > 0, there are infinitely many solutions.

When x = 0, there is only one solution.

When x < 0, there are no solutions.

In this case, x = 7, and 7 > 0. Therefore there are infinitely many solutions.