Question

What type of system of linear equations is this?

y = –5x – 4
y=1/2x+3
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A. consistent and independent
B. consistent and dependent
C. inconsistent
D. independent and inconsistent

(this is all the ino the question gives me, there's no graph or anything)

Answer 1

Option A is correct.

Explanation:

y =-5x -4

y=
`(1)/(2)`x+3

As we know that slope intercept form of line is y =mx+b

where m = slope and b = Y intercept.

on comparing the equations given with standard equation ,we get

for first equation ; slope = 5 and Y intercept = -4

for Second equation; slope =
`(1)/(2)`

And we know that if slope and Y intercept of two equations are distinct

then solution is consistent and independent .

Here we can see that slope and intercept of both equations are different

therefore system of equations is consistent and independent.

option A is correct.

Answer 2

y = -5x - 4....slope = -5 and y int = -4
y = 1/2x + 3...slope = 1/2 and y int = 3

if the slopes and the y intercepts are different, then there is 1 solution making this independent and consistent