SOLUTION: What is the solution set for the system of inequalities 3X2-4X-5 < Y and 4X+3Y< 2? A. -1 < X < 2 B. -1 < X < 17/9 C. -0.79 < X < 2.12 D. -1 < X < 0.5

Algebra ->  Linear-equations -> SOLUTION: What is the solution set for the system of inequalities 3X2-4X-5 < Y and 4X+3Y< 2? A. -1 < X < 2 B. -1 < X < 17/9 C. -0.79 < X < 2.12 D. -1 < X < 0.5      Log On


   

Question 696476: What is the solution set for the system of inequalities 3X2-4X-5 < Y and 4X+3Y< 2?
A. -1 < X < 2

B. -1 < X < 17/9

C. -0.79 < X < 2.12

D. -1 < X < 0.5


Found 2 solutions by MathLover1, SkinnyPrincess:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2-4x-5+%3C+y.......1.... and
4x%2B3y%3C+2..............2
______________________
3x%5E2-4x-5+%3C+y.......1.set y=0
3x%5E2-4x-5+%3C+0..solve as equation to find x
3x%5E2-4x-5+=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A3%2A%28-5%29+%29%29%2F%282%2A3%29+

x+=+%284+%2B-+sqrt%2816%2B60+%29%29%2F6+
x+=+%284+%2B-+sqrt%2876+%29%29%2F6+
x+=+%284+%2B-+8.7177978870813471044739639677192%29%2F6+
solutions:
x+=+%284+%2B+8.7177978870813471044739639677192%29%2F6+
x+=+%2812.718%29%2F6+
x=2.12

x+=+%284+-+8.718%29%2F6+
x+=+%28-4.718%29%2F6+
x=-0.79
so, -0.79%3Cx%3C2.12

3y%3E-4x%2B2..............2..set y=0
0%3E-4x%2B2
4x%3E2
x%3E2%2F4
x%3E1%2F2
system solution is
C. -0.79%3Cx%3C2.12
+graph%28+600%2C+600%2C+-6%2C+10%2C+-10%2C+10%2C+%284%2F3%29x-+2%2F3%2C+3x%5E2-4x-5%29+

Answer by SkinnyPrincess(1) About Me  (Show Source):
You can put this solution on YOUR website!
This is a wrong answer. According to teacherstestprep.com , CSET Math practice test #9, the answer should be B) -1 < X < 17/9
Whoever answered earlier had the 2nd equation mixed up 4X+3Y< 2 ==> when y = 0, x < 1/2 (NOT x > 1/2, not important) . And, the slope of 2nd equation should be negative, so the graph is wrong.
in order to find the X values when Y values are same ==> combine 2 equations together 4x + 3(3X^2-4X-5) = 2
simplify to 9X^2 - 8x - 17 = 0
(x + 1)(9x - 17) = 0
x = -1 and 17/9