Question

Which of the following points is a solution to a system of linear equations

y<3x+5
y>-2/3x-3
_
a.(3,14)
b.(3,9)
c.(3,-14)
d.(3,-9)

Answer 1

b) The ONLY solution for the given system is (3,-9).

Explanation:

Here, the given set of equation is:

`y< 3 x+5\\y > (-2)/(3)x -3`

Now, let us check the given equation for each given point, we get:

(a) For (x, y) = (3,14)

Putting the above values in the given equation y < 3x + 5:

when x = 3, 3x + 5 = 3(3) + 5 = 14

and for y = 14, 14 is NOT LESS THAN 14

So, (3,14) is NOT a solution.

(b) For (x, y) = (3,9)

Putting the above values in the given equation y < 3x + 5:

when x = 3, 3x + 5 = 3(3) + 5 = 14

and for y = 9, 9 < 14

Putting the above values in the given equation y > -2/3x - 3:

when x = 3,
`(-2)/(3) x -3 = (-2)/(3) (3)  -3 = -2 -3  = -5`

and for y = 9, 9 > -5

Hence, (3,9) is a solution.

(c) For (x, y) = (3,-14)

Putting the above values in the given equation y < 3x + 5:

when x = 3, 3x + 5 = 3(3) + 5 = 14

and for y = -14, -14 < 14

Putting the above values in the given equation y > -2/3x - 3:

when x = 3,
`(-2)/(3) x -3 = (-2)/(3) (3)  -3 = -2 -3  = -5`

and for y = -14 , -14 is NOT GREATER then -5.

So, (3,-14) is NOT a solution.

(d) For (x, y) = (3,-9)

Putting the above values in the given equation y < 3x + 5:

when x = 3, 3x + 5 = 3(3) + 5 = 14

and for y = -9, -9< 14

Putting the above values in the given equation y > -2/3x - 3:

when x = 3,
`(-2)/(3) x -3 = (-2)/(3) (3)  -3 = -2 -3  = -5`

and for y = -14 , -9 is NOT GREATER then -5.

So, (3,-9) is NOT a solution.

Hence, the ONLY solution for the given system is (3,-9)