In this document, we'll revisit the core concepts, delve into various solution methods, and provide practical tips to bolster your skills in solving simultaneous equations. Through interactive practice exercises, you'll gain the confidence needed to excel in your Grade 10-12 math curriculum. Whethe...
**Problem 1:**
Equations:
1. 2x + y = 10
2. x - 3y = 1
Solution:
From equation 2, we can express x in terms of y: x = 3y + 1.
Substitute x in equation 1: 2(3y + 1) + y = 10.
Simplify: 6y + 2 + y = 10.
Combine like terms: 7y + 2 = 10.
Subtract 2 from both sides: 7y = 8.
Divide by 7: y = 8/7.
Substitute y back into x = 3y + 1: x = 3(8/7) + 1.
Simplify: x = 24/7 + 1.
Common denominator: x = (24 + 7)/7.
Simplify: x = 31/7.
Solution:
Multiply equation 2 by 3 to match the coefficient of y: 6x - 3y = 21.
Add equation 1 to the modified equation 2: 4x + 3y + 6x - 3y = 20 + 21.
Combine like terms: 10x = 41.
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