Question

Solve this equation using elimination:

2X + 3Y = 16
6X - 5Y = 20

Answer 1

Another bag of marbles contains 6 blue marbles and 1 green marble. Mary and Frank will draw a blue marble followed by a green marble, without replacing the first marble. Mary says the probability will be 649, and Frank says that the probability will be17 . Who is correct?

Answer 2

(5, 2 )

Explanation:

Given the 2 equations

2x + 3y = 16 → (1)

6x - 5y = 20 → (2)

Multiplying (1) by - 3 and adding to (2) will eliminate the x- term

- 6x - 9y = - 48 → (3)

Add (2) and (3) term by term to eliminate x

0 - 14y = - 28

- 14y = - 28 ( divide both sides by - 14 )

y = 2

Substitute y = 2 into either of the 2 equations and solve for x

Substituting into (1)

2x + 3(2) = 16

2x + 6 = 16 ( subtract 6 from both sides )

2x = 10 ( divide both sides by 2 )

x = 5

solution is (5, 2 )