Question

Solve the following system of equations by the elimination method:

2x + 5y = 9, x – y = 1

Answer 1

Given system of equations:

2x + 5y = 9

x – y = 1

Step 1: Multiply the second equation by 2 to align the coefficients of (x):

2(x – y) = 2 × 1

⇒ 2x – 2y = 2

Step 2: Subtract this new equation from the first equation to eliminate (x):

(2x + 5y) – (2x – 2y) = 9 – 2 

⇒ 2x + 5y – 2x + 2y = 7

⇒ 7y = 7

Step 3: Solve for (y):

7y = 7 

⇒ y = 1

Step 4: Substitute (y = 1) back into the second original equation:

x – 1 = 1 

⇒ x = 2

The solution to the system is x = 2, y = 1.