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Simultaneous linear equations
Two equations, two unknowns. Combine the equations to knock one letter out, then the other one is easy to find.
Eliminate one letter
Line the equations up. If one letter has the same number in front of it in both:
Same signs, subtract. Different signs, add.
Same signs, subtract. Different signs, add.
Make the numbers match
If no letter matches yet, multiply one equation (or both) so it does.
4x + 3y = 25 and 2x + y = 11
Double the second: 4x + 2y = 22. Now the x terms match.
4x + 3y = 25 and 2x + y = 11
Double the second: 4x + 2y = 22. Now the x terms match.
Substitute back and check
Put your first answer into either equation to find the other letter. Then check both values in the other equation.
Solve 3x + 2y = 16 and x + 2y = 8
- Both have +2y. Same signs, so subtract: (3x − x) = 16 − 8
- 2x = 8, so x = 4
- Substitute into x + 2y = 8: 4 + 2y = 8, so y = 2
- Check in the first equation: 3 × 4 + 2 × 2 = 16. Correct.
Answer: x = 4, y = 2
Match one letter's coefficients, then same signs subtract, different signs add. Find the first letter, substitute back, and check in the other equation.
Check you have got it
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