Question

Determine whether this system of equations has one solution, no solution, or infinitely many solutions. y=8x+2 y=-8x+2

Answer 1

1.) First start by looking at your slopes
A.) They are the same, so keep that in mind.
2.) are the initial values (b) different or the same?
A.) They are the same.
Now we can determine that the variables and initial values are the same, meaning that the two equations overlap on a graph. This means there are infinity solutions! :)

Answer 2

Explanation:

Since you already have y isolated in one equation, you can plug it in and use it in the other equation2y = 8x + 122(4x + 6) = 8x + 128x + 12 = 8x + 12Get the x's to one side 12 = 12Meaning you have infinitely many solutions. Try plugging in any x value you can think of and the left side will always equal the right side. sox = 0 --> 8(0) + 12 = 8(0) + 1212 =12x = 1 --> 8(1) + 12 = 8(1) + 1220 = 20and so on.I graphed it here for you and the 2 functions are on top of each other which means at every x value y = 4x + 6 is equal to 2y = 8x + 12