System of Equations Calculator
Equation 1:
x +
y =
Equation 2:
x +
y =
Result
Solution Methods
1. Elimination Method
Multiply equations to make coefficients of one variable equal, then subtract to eliminate that variable.
2. Substitution Method
Solve one equation for one variable, then substitute into the other equation.
3. Matrix Method
Convert system to matrix form and use row operations to solve.
Example Problems
Example 1:
2x + y = 5
x - y = 1
Solution Steps (Elimination):
- Add equations: 3x = 6
- Solve for x: x = 2
- Substitute x = 2 into first equation: 2(2) + y = 5
- Solve for y: y = 1
Solution: x = 2, y = 1
Example 2:
3x - 2y = 4
x + y = 3
Solution Steps (Substitution):
- From equation 2: x = 3 - y
- Substitute into equation 1: 3(3 - y) - 2y = 4
- Solve: 9 - 3y - 2y = 4
- 9 - 5y = 4
- y = 1
- Substitute back: x = 2
Solution: x = 2, y = 1
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