Systems of Equations in Two Variables
Q: What is a system of equations?
A: A system of equations is a collection of
two or more equations that are to be solved simultaneously.
- A solution to a system of equations in
two variables is an ordered pair which is a solution to
ALL of the equations in the system.
1. Is ( 2 ; 1 ) a solution of the system below?
2x - 3y = 1
x + 6y = 8
2. Is ( -2, 2 ) a solution of the system below?
3x + 3y = 0
4x - 2y = 12
- What it all comes down to is this: A solution to a system
of linear equations in two variables is the point of
intersection of two lines. When we graph two lines, there
are actually three possibilities (as far has how they
intersect is concerned).
- They intersect in one point.
In this case, there is one solution to the system.
- The lines are parallel (do not intersect).
In this case, there is no solution to the system.
In this case, the system has infinitely many solutions (every
point on the line).