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Question 568968: What is System of Linear Equation in Two Variables ?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! A linear equation in two variables is an equation with two variables (usually called x and y) where the variables are at most multiplied by a number, and added to something else. No exponents, no variables in denominators, no fancy functions of the variables.
For example 2x-y=3 and x+y=3 are linear equations.
A set of linear equations is a system of linear equations. A typical set of linear equations in two variables is:
2x-y=3
x+y=3
As the name hints, a linear equation in two variables gives you a straight line when you plot points for data pairs (x,y) that satisfy the equation. With two of those linear equations, you could expect to get two straight lines. Their intersection would represent the solution to the system of equations.
The graph for the two equations could be the same line (if the equations are equivalent to each other, like x+y=3 and 2x+2y=6). Then you would have infinite solutions, represented by all the points in the common line.
You could also end up with two parallel lines, that have no point in common, and the system would have no solution.
In the case of 2x-y=3 and x+y=3, the straight lines representing those equations cross at a point that belongs to both lines. That point represents the solution to the system made of those two equations. The point (2,1), with x=2 and y=1, is the intersection of the graphs for the equations above and the solution of the system of equations. The set of variable values x=2 and y=1 satisfies both equations.
How to graph linear equations and how to solve a system of linear equations could be your next questions. I am just glad that I do not have to answer them, at least for now.
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