Adding equations when you should subtract
"The Operation Confusion"
The Mistake in Action
Solve: $4x + 3y = 17$ ... (1) and $4x + y = 11$ ... (2)
Wrong: Add: $8x + 4y = 28$
Why It Happens
Students see matching coefficients and automatically add, without considering whether adding or subtracting will eliminate the variable.
The Fix
Look at the signs of the matching coefficients:
- Same signs (+4x and +4x) → Subtract to eliminate
- Opposite signs (+4x and -4x) → Add to eliminate
Here both have $+4x$, so subtract: (1) − (2): $2y = 6$, so $y = 3$
Memory aid: "Same signs, subtract. Different signs, add."
Spot the Mistake
Can you identify where this student went wrong?
$4x + 3y = 17$ and $4x + y = 11$
Add: $8x + 4y = 28$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: