Solve the System of Inequalities

Elimination method

3x +4y ≥ 0

2x +3y ≥ 1

Multiply by 2, -3

6x +8y ≥ 0

-6x +-9y ≥ -3

Add

-1y ≥ -3

y = 3

3x + 12≥ 0

3x + ≥ -12

x = -4

y = 3 x = -4

First we need to find the common denominator of the left side of the equation so that we can combine the terms. The second term is just 5 which can also be written as 5/1.

The common denominator is x+2, so we need to multiple both the numerator and denominator of 5/1 by x+2:

5x/(x+2) - (5*(x+2))/(1*(x+2))

5x/(x+2) - (5x+10)/(x+2)

Now subtract the numerators:

(5x - (5x + 10))/(x+2)

(5x - 5x - 10)/(x+2)

-10/(x+2)

Now we have one fraction equal to another fraction, so we can solve the proportion for x by cross multiplying.

-10/(x+2) = (x-11)/(x-2)

-10(x-2) = (x-11)(x+2)

Distribute:

-10x + 20 = x^2 + 2x - 11x - 22

Combine:

-10x + 20 = x^2 - 9x - 22

x^2 + x - 42 = 0

Factor:

(x+7)(x-6) = 0

x = -7 or x = 6