System of Equations
Solve linear systems of two unknowns (2x2).
Solve systems of linear equations with two equations (2x2):
x +y =
x +y =
What is a 2x2 Linear System?
In mathematics, a 2x2 linear system is a set of two first-degree equations that share the same two unknown variables (usually called X and Y). The goal of solving a system is to find the unique value of X and Y that makes both equations true at the same time.
Simple Example (Buying Fruits)
Imagine that you don't know the price of the Apple (X) or the Banana (Y), but you know that:
- 1 Apple + 2 Bananas = R$ 5 (1x + 2y = 5)
- 2 Apples + 1 Banana = R$ 7 (2x + 1y = 7)
If you plug these numbers into our calculator (Equation 1: a=1, b=2, c=5 and Equation 2: d=2, e=1, f=7), the tool will execute Cramer's Rule and find that the Apple costs R$ 3 (X=3) and the Banana costs R$ 1 (Y=1).