Question

Consider the system of equations 2x + 5y = 5 and -3x + 7y = 7. What number would you multiply to eliminate the y?

Answer 1

(0, 1 )

Explanation:

2x + 5y = 5 → (1)

- 3x + 7y = 7 → (2)

to eliminate y multiply (1) by 7 and (2) by - 5 , then add the result

14x + 35y = 35 → (3)

15x - 35y = - 35 → (4)

add (3) and (4) term by term to eliminate y

29x + 0 = 0

29x = 0 ⇒ x = 0

substitute x = 0 into (1) and solve for y

2(0) + 5y = 5y

0 + 5y = 5

5y = 5 ( divide both sides by 5 )

y = 1

solution is (0, 1 )