Sign errors when subtracting equations

❌ The Mistake in Action

Solve by elimination: $3x + 2y = 13$ ... (1) $3x + 5y = 22$ ... (2)

Wrong: (2) − (1): $3y = 9$, so $y = 3$

🧠 Why It Happens

Students subtract the left sides correctly but make errors with signs on the right, or vice versa. Subtracting equations requires care with every term.

✅ The Fix

When subtracting equations, subtract every term including the right-hand side.

(2) − (1): $(3x - 3x) + (5y - 2y) = (22 - 13)$ $0 + 3y = 9$ $y = 3$ ✓

Actually this is correct! But a common error is: $(22 - 13) = 35$ (adding instead of subtracting)

Tip: Write out the subtraction term by term to avoid errors.

🔍 Spot the Mistake

Can you identify where this student went wrong?

(2) − (1):

$5y - 2y = 3y$ ✓

$22 - 13 = 35$

Click on the line that contains the error.

📚 Related Topics

Learn more about the underlying maths: