How many solutions does this have? 2x + 3 = 4x + 2

no solutions

one solution

many solutions

2x+3=4x+2

-2 - 2

2x+1=4x

-2x - 2x

1=2x

(divide both sides by 2)

.5 = x (one solution)

There are a couple of ways you can rule out different amounts of solutions in a system of linear equations.

1. If the slope and y-intercept is the same, there are many solutions.

2. If the slopes are the same, but the y-intercept isn't, there is no solution.

3. If there are no similarities, there is only 1 solution.

Since the equation only applies to 3, there is one solution.