Question

How many soultions does the system of equations have

y= -6x + 3
30x + 5y = 15

a.one
b.two
c.infinity many
d.none

Answer 1

C. infinity many

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

If the equations have the same slopes and the same y-intercepts, then the system of equations has infinitely many solutions.

If the equations have the same slopes and differences of the y-intercepts, then the system of equations has no solution.

If the equations have different slopes, then the system of equations has one solution.

We have

`y=-6x+3` → m = -6 and b = 3

and

`30x+5y=15`

convert to the slope-intercept form:

`30x+5y=15` subtract 30x from both sides

`5y=-30x+15` divide both sides by 5

`y=-6x+3` → m = -6 and b = 3

We have the same slopes and the same y-intercepts.