Simultaneous equations calculator
3x + 2y = 16 and 2x − y = 6
x = 4, y = 2
The lines cross at (4, 2).
Working
- (1) 3x + 2y = 16
- (2) 2x − y = 6
- (2) × 2: 4x − 2y = 12 (4)
- The y terms have opposite signs, so add the equations: 7x = 28, so x = 28 ÷ 7 = 4.
- Substitute x = 4 into (1): 2y = 16 − 12 = 4, so y = 2.
- Check in (2): 2 × 4 + (−1) × 2 = 6 ✓
Your result
x = 4, y = 2. The lines cross at (4, 2).
Simultaneous equations, step by step
GCSE Maths Pro
Get a grade 8 or your money back
£119 once
No VAT is charged. Conditions
Your mock plan, in three taps
Solve simultaneous equations by elimination: 3x + 2y = 16 and 2x − y = 6 give 7x = 28, so x = 4 and y = 2.
Questions people ask
How do you solve simultaneous equations by elimination?
Make the number in front of x or y the same in both equations by multiplying. Add the equations if the signs are different, subtract if they are the same. Solve for the variable that is left, then substitute it back to find the other.
When do you add and when do you subtract?
Same signs subtract, different signs add. 2y and 2y: subtract. 2y and −2y: add.
What if the equations are not in the form ax + by = c?
Rearrange them first so x and y are on the left and the number is on the right. y = 2x − 1 becomes −2x + y = −1.
What does it mean if there is no solution?
The two lines are parallel, so they never cross. If the equations are multiples of each other, they are the same line and every point on it is a solution.
More free tools
Keep going
How we work this out
What it does
Enter two linear equations to solve them by elimination, with every step written out and the answer checked.
Two linear equations ax + by = c with whole-number coefficients.
Method
- Multiply one or both equations so the y coefficients match.
- Add the equations if the y terms have opposite signs, subtract if the same, then solve for x.
- Substitute x into an original equation for y, and check in the other.