System of Equations Solver

2x + 3y = 12 and x - y = 1 Substitution: x = 1 + y from Eq2 2(1 + y) + 3y = 12 2 + 2y + 3y = 12 5y = 10, y = 2 x = 1 + 2 = 3 Solution: (3, 2)

A system of linear equations involves two or more linear equations that share the same set of variables. In simpler terms, you are looking for specific values for each variable that will satisfy every equation in the system simultaneously. For a system of two linear equations with two variables, often denoted as x and y, this translates geometrically to finding the point where two lines intersect on a coordinate plane. Each equation represents a distinct line, and their intersection point is the unique solution where both conditions are met. If the lines are parallel and never intersect, there is no solution. If the lines are identical, they intersect at every point, leading to infinitely many solutions. Algebraically, the two most common methods to find these solutions are substitution and elimination. Substitution involves solving one equation for a variable and plugging that expression into the other equation. Elimination, on the other hand, aims to cancel out one variable by adding or subtracting the equations, often after multiplying one or both by a constant. These techniques are fundamental in algebra for solving problems where multiple conditions must be satisfied concurrently.