System of Linear Equations:
A system of linear equations or system of equations means two or more linear equations that are being solved simultaneously.
What is the solution of a system of equations?
A system of linear equations or system of equations means two or more linear equations that are being solved simultaneously.
What is the solution of a system of equations?
When two equations meet or intersect at a point then this point is called solution of the system.
A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases.
One solution:
This is the most common situation. Here, two lines meet at one point.
6x − 2y = 8
4x + y = −1
Since the lines intersect exactly once, the system has exactly one solution.
No solution:
A system of linear equations has no solution when the graphs are parallel.
y = −x + 6
5x + 5y = 15
We see two distinct parallel lines. We can confirm that the lines are indeed parallel, since the slopes of both lines are equal to −1. Since distinct parallel lines don't intersect, we conclude that the system has no solutions.
Infinite solutions:
A system of linear equations has infinite solutions when the graphs are the exact same line.
2x + y = 5
14x + 7y = 35
The two lines are the same, they intersect infinitely many times. This means that the system has infinitely many solutions.
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