Question

Solve 2x - y = 13

3x + y = 12

A. (9,5)

B. (5, -3)

C. ( -19, -3)

D. ( -3, 5)

Answer 1

B

Given the 2 equations

2x - y = 13 → (1)

3x + y = 12 → (2)

add (1) and (2) term by term to eliminate the term in y

5x = 25 ( divide both sides by 5 )

x = 5

substitute x = 5 in either of the 2 equations and solve for y

(2) : (3 × 5 ) + y = 12

15 + y = 12 ( subtract 15 from both sides )

y = - 3

solution is (5, - 3 ) → B

Answer 2

2x - y = 13 ------------- [1]

3x + y = 12 ------------ [2]

Adding both Equations [1] and [2], We get :

⇒ (2x - y) + (3x + y) = 13 + 12

⇒ 2x + 3x - y + y = 25

⇒ 5x = 25

⇒ x = 5

Substituting x = 5 in Equation [1], We get :

⇒ 2(5) - y = 13

⇒ 10 - y = 13

⇒ y = 10 - 13

⇒ y = -3

⇒ (x , y) = (5 , -3)

Option B is the Answer