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Question
Solve the following system of equations by the elimination method:
2x + 5y = 9, x – y = 1
Sum
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Solution
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.
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