Question:
2x + y = 3, x - 2y = –1.
If equation one is multiplied by 2 and then the equations are added, the result is _____.
(A) 3x = 2
(B) 3x = 5
(C) 5x = 5
Answer:
Option C:
5x = 5
Solution:
Given equations are
2x + y = 3 – – – – (1)
x – 2y = –1 – – – – (2)
Let us first multiply equation (1) by 2, we get
(1) × 2 ⇒ 4x + 2y = 6 – – – – (3)
Now, add equation (3) to equation (2).
⇒ x – 2y + 4x + 2y = –1 + 6
Combine like terms together.
⇒ x + 4x – 2y + 2y = –1 + 6
⇒ 5x = 5
So, if equation one is multiplied by 2 and then the equations are added, the result is 5x = 5.