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

Answer:

C. infinity many

Step-by-step 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.