Question

please help...im desperate
Choose the point which is a solution to the system of inequalities:

x - 2y > -16
3x + 4y < 20

(8, 3)
(-2, 7)
(-4, -6)
(11, -1)

Answer 1

one method
plug the numbers and see which set of values satisfies both inequalities

another more preferable method
set the inequality as =
solve the simultaneous eqn by substitution, elimination or graphing
use the values as the limits to satisfy the inequalities
find the intersection of both and that will be the solution

to solve by substitution
using the first eqn let x = -16 +2y
substitute in the 2nd inequality and solve
3x + 4y < 20
3(-16 +2y) <20
substitute this y value and find x

to solve by elimination
set = 0
multiply the 1st eqn by 2 and add to the 2nd
add, group like terms, simplify, solve then substitute
satisfy the inequality and find the intersection

to solve by graphing
rewrite each in the form y as a function of x
set up values of x and find the corresponding value of y then plot the points and draw the lines shade the section that satisfies the inequality
the solution is the section that is double-shaded.
finding the

Answer 2

the 1st method is fast in an exam , the answer is right there
also note that if the values do not work for one system automatically go to the next

the 2nd approach will always work. once you know how to do it and which method you prefer it's just as easy