Question

The point (4, 1) is a solution to which of the following systems of inequalities?

a. y < 3x - 1 and y > -x + 1
b. y > 3x - 1 and y > -x + 1
c. y > 3x - 1 and y < -x + 1
d. y < 3x - 1 and y < -x + 1

I'm very confused:( I don't know how to solve this. Please help? Thanks

Answer 1

test your point in each of the cases.
I will try c)
is 1 > 12-1 and 1 < -4+1
is 1 > 11 and is 1 < -3
I guess not! , so not c)

remember , since they use the logical operator "and", both parts must be true

Answer 2

Ah, okay.
So, would the answer be d?
1 < 12-1 and 1 < -4 + 1
1 < 11 and 1 < -3

Answer 3

Wait... 1 < -3

Answer 4

It's a

Answer 5

1<11
and
1>-3
:) yes a

Answer 6

correct, it is a)

another way would be to look at the regions that each defines and see if the point lies in that region.
since you only have two boundaries to worry about, that would be quite easy.
So sketch y = 3x -1 , (y-intercept of -1 and slope of 3)
and y = -x+1 , (y-intercept of 1 and slope of -1)
to see that (4,1) lies below y = 3x -1 ( < )
and above y = -x+1 , (>)

Answer 7

Thank you, Reiny and Damon!!:) I easily understand it now