What is the point for the inequality of 3x+2y<15; 7x-4y>9?

Question

(3x+2y<15)

(7x-4y>9)

X= ?

Y= ?

Answer 1

2y < 15 - 3x

y < (-3/2)x + 15/2

intercept point at (0,15/2)

go down three and 2 to the right...

DASHED LINE, crosses the x-axis at (5,0)

Testing (0,0): 3(0) + 2(0) > 15

0 + 0 > 15

0 > 15 FALSE

shades AWAY form the origin

7x - 4y > 9

7x - 9 - 4y > 0

7x - 9 > 4y

(7/4)x - 9/4 > y

intercept point at (0, -9/4)

Go up 7 and 4 to the right

DASHED LINE, crosses the x-axis at (9/7,0)

Tests (0,0): 7(0) - 4(0) > 9

0 - 0 > 9

0 > 9 FALSE

shades away from the origin

Now for the intersection point:

3x+2y = 15

7x - 4y = 9

Multiplies top equation by 2, and then adds them together

6x + 4y = 30

7x - 4y = 9

13x = 39

x = 3

3(3) + 2y = 15

9 + 2y = 15

2y = 6

y = 3

check: 7(3) - 4(3) = 21 - 12 = 9

intersection is at (3,3)

So the solution are where the two regions overlap.

The triangular portion of the solution crosses (1.286, 0), (3,3), and (5,0)

picture located in the RESOUCES section under toolkit, names TWO INEQUALITIES.jpg