How many soultions

Question

How many solutions does the following system of equations have?
2y=5x + 4
y=3x + 2
A.) Two
B.) Zero
C.) One
D.) Infinitely many

Answer 1

For a question like this, all you need to do is find the slope and y-intercept by solving for y. Most of the time, you just need to get the slope of each equation.

In this case, the slope of the first equation is 5/2 and the slope of the second is 3.

If the equations have different slopes, then there is only ONE solution.
If the equations have the same slope, but a different y-intercept, there are NO solutions (parallel lines).
If the equations have the same slope and same y-intercept, there are infinitely many solutions (overlapping lines).

Answer 2

the slopes are different. this system is consistent so there is one solution