Multiplying only one side of an equation
"The One-Sided Multiply"
The Mistake in Action
Solve: $x + 2y = 5$ ... (1) and $3x + 4y = 11$ ... (2)
Wrong: Multiply (1) by 3: $3x + 2y = 5$
Why It Happens
Students multiply the $x$ term to match coefficients but forget to multiply the entire equation — including the $y$ term and the constant.
The Fix
When multiplying an equation, multiply EVERY term on both sides.
(1) × 3: $$3(x) + 3(2y) = 3(5)$$ $$3x + 6y = 15$$
Now you can eliminate $x$ by subtracting from equation (2).
Spot the Mistake
Can you identify where this student went wrong?
Multiply (1) by 3 to match the x coefficients
$3x + 2y = 5$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: