Question

Please helpWithout graphing, classify the following system as independent, dependent, or inconsistent.

-21x-3y=-24

y=-7x+7

a.independent
b.dependent
c.inconsistent

Answer 1

from the first equation you can take out 3 as a common factor and reduce it to y = -7x+8.
Combined with y = -7x +7 what kind of system does it form?

Answer 2

parallel lines with a slope of -7

Answer 3

ok so its indepent

Answer 4

for a system of linear equations

a1x + b1y + c1 = 0 and
a2x + b2y + c2 = 0

if a1/a2 not equal to b1/b2 - the two lines meet at a point and have unique solution - so consistent and independent

if a1/a2 = b1/b2 = c1/c2 - the two lines coincide and so infinite solutions - so consistent and dependent

if a1/a2 = b1/b2 not equal to c1/c2 - the two lines are parallel and hence no solution - so inconsistent

Answer 5

o ok thank you very much

Answer 6

Your given equations can be written as

-21x-3y + 24 = 0 and
7x + y - 7 = 0

a1/a2 = -21/7 = -3/1

b1/b2 = -3/1

c1/c2 = 24/-7 = -24/7

so

a1/a2 =b1/b2 not equal to c1/c2
so two lines are parallel--hence no solution--hence inconsistent

Answer 7

@Harkirat Can you help me with one more question.

Graph the system of inequalities, Which two quadrants does the solution lie in?

y > x+2

y<-x+1

A.Quadrants 2 and 3
B.Quadrants 3 and 4
C.Quadrants 2 and 4
D.Quadrants 1 and 2

Answer 8

i think B.Quadrants 3 and 4

Answer 9

You will have to plot the graphs to see how it turns out....

Answer 10

@Harkirat yeah I need help, how do you know what quadrants because the lines go in different directions