16) Will somebody please help me with an Algebra problem?

Question

Check whether the given ordered pairs are solutions of the inequality.

y < -9x + 7; (-2,2), (3, -8)

Answer 1

y < - 9x + 7

RHS = - 9 x + 7 = 18 + 7 = 25
LHS = 2
2 < 25
Thus (- 2 , 2) IS a solution.

RHS = - 9 x + 7 = - 27 + 7 = - 20
LHS = - 8
- 8 is not less than - 20
Thus (3 , - 8) is NOT a solution.

Answer 2

What you have to do is to fill in the given pair in the inequality and see if the result makes sense.
So:

2<-9(-2)+7
2<25 that's correct, (-2,2) is a valid solution

-8<-9(3)+7
-8<-20 That's wrong, (3,-8) is not a solution

Answer 3

For the first ordered pair (-2, 2):
substitute y by 2 and x by -2, you get
2 < -9(-2)+7
2 < 18 + 7
2 < 25 which is true, so (-2, 2) is a solution

For the second ordered pair (3, -8):
substitute y by -8 and x by 3, you get
-8 < -9(3) + 7
-8 < -27 + 7
-8 < -20 which is false, so (3, -8) is not a solution.

Answer 4

Plugging in the numbers you have, in the two cases:

1) (-2,2):

2 < 18 + 7
2 < 25

Wich is true, so that pair, IS a solution.

2) (3,-8)

-8 < -27 + 7
-8 < - 20

Which is FALSE so the second pais IS NOt a solution.

Moreover, if you trace on a Cartesian plane the line decribed by y=-9x+7, you'll notice that any pair of numbers that constitutes the coordinates of a point which is UNDER that line (just like -2;2), will verify that inequality, on the other side, every point OVER that line (like 3;-8) will have coordinates that DO NOT verify that inequaity.

In that way you'll have a quick eye view of EVERY SINGLE couple of numbers which, representing the coordinates of a point, will verify that inequality. Cool, huh? Lol maybe not...

Answer 5

y < -9x + 7; (-2,2), (3, -8)

First: substitute the 1st set of numbers in the inequality
(x = -2 & y = 2).

2 < -9(-2) + 7
2 < 18 + 7
2 < 25
True

SEc: substitute the 2nd set of numbers in the inequality
(x = 3 & y = -8).

-8 < -9(3) + 7
-8 < -27 + 7
- 8 < -20
False (-20 is farther away from "0" on a number line, than -8)

Answer 6

Using the first pair (x=-2, y=2), we have
2 < -9( -2 ) + 7
2 < +18 +7
2 < 25
which is true

For the second pair (x=3, y=-8), we get:
-8 < -9(3) + 7
-8 < -27 +7
-8 < -20
which is false.

Answer 7

y < -9x + 7

First ordered pair:
x = -2
y = 2

Substitute in equality:

2 < -9(-2) + 7 --> 2 <18 + 7 --> 2 < 25

True, hence solution.

Second ordered pair:
x = 3
y = -8

Substitute in equality:

-8 < -9(3) + 7 --> -8 < -27 + 7 --> -8 < -20

Untrue, hence not a solution.

Answer 8

All you need to do is place the values into the inequality and simplify.
(x, y)

So...
(-2, 2) means x = -2 and y = 2

y < -9x + 7
2 < -9(-2) + 7
2 < 18 + 7
2 < 25 TRUE, so that point is a solution.

Now you try the other one.

Answer 9

well for -2,2
we have 2<(-9)*(-2)+7
which is 2<25- i.e true

for 3,-8
-8<-9*3+7
-8<-20, i.e. false
-20 is smaller than -8 not greater.

hope that helps.