Mathematics / Simultaneous Equations
A linear equation is an algebraic equation that contains terms which can either be constants or variables. The variables can only be of the first power.
A linear equation in two variables is of the form ax + by + c = 0, where x and y are variables and a, b and c are real numbers. Additionally a and b are non zero.
The graph of a linear equation in two variables plotted on a Cartesian plane is a straight line.
Given a pair of linear equations, they can be plotted as two lines in the Cartesian plane.
- If the two lines intersect, the pair of equations is said to be consistent. Solving the two equations simultaneously yields a unique value for each of the two variables. These values represent the co-ordinates of the point of intersection.
- If the two lines are parallel, the equations are inconsistent and there is no solution.
- If the two lines are coincident, then there are infinite solutions since every point on these lines is a point of intersection and as we know the line extends infinitely.
Simultaneous Linear Equations in Two Variables
- Simultaneous Equations
- Simultaneous Linear Equations in Two Variables - Graphical Method
- Simultaneous Linear Equations in Two Variables - Algebraic Method
Simultaneous Equations - Practical Applicatio
Pair of Linear Equations - Algebraic Method