Two equations with two unknowns
Two equations, two unknowns: the solution is the point where the two lines cross. Enter the coefficients and see both the working and the graph.
Your numbers
a₁x + b₁y = c₁
a₂x + b₂y = c₂
1x + 1y = 10
1x − 1y = 2
Answer
x
6
y
4
How to work it out
- 1D = a₁·b₂ − a₂·b₁ = 1·-1 − 1·1 = -2
- 2Dx = c₁·b₂ − c₂·b₁ = 10·-1 − 2·1 = -12
- 3Dy = a₁·c₂ − a₂·c₁ = 1·2 − 1·10 = -8
- 4x = Dx / D = 6 · y = Dy / D = 4
- 5Test: 10 = 10 · 2 = 2
The formula
x = Dx / D · y = Dy / D
The determinant method. D is a₁·b₂ − a₂·b₁; if it is 0, the lines are parallel.
Elimination method
Add the equations or subtract one from the other, so that one unknown disappears.
The copper line is the first equation, the dashed one the second. The solution is where they cross.
More: Equations and functions
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