Question

8x - 3y < 4
9.x + 2y <-1
is (5, -5) a solution of the system?

Answer 1

Answer: No, it is not a solution

Step-by-step explanation:

Plug (x,y) = (5,-5) into the first inequality and simplify

8x-3y < 4

8(5) - 3(-5) < 4 ... x replaced with 5, y replaced with -5

40 + 15 < 4

55 < 4 ... this is false as 55 is not smaller than 4

We get a false statement after simplifying both sides. Therefore, (5,-5) is not a solution to the system of inequalities. For it to be a solution, it would need to make both inequalities true after plugging in the x and y coordinates.

We don't need to check the other inequality since the first inequality was shown to be false.

Answer 2

Answer: 4x − 2y = 6 . . . . . (1)

2x + y = 5 . . . . . (2)

(2) x 2 => 4x + 2y = 10 . . . . . (3)

(1) - (3) gives: -4y = -4

y = -4/-4 = 1

From (2), 2x + 1 = 5 => 2x = 5 -1 = 4

x = 4/2 = 2

Solution is (2, 1)

Substituting the solution into the options gives that

−4x − 2y = 10

−4y = 4 −4x

has the same solution.

hope this helped!! :)