A system of linear equations means two or more linear equations. (In plain speak: 'two or more lines') If these two linear equations intersect, that point of intersection is called the solution to the system of linear equations.
What is a system of equations?Answer
A system of equation just means 'more than 1 equation.'. A system of linear equations is just more than 1 line, see the picture:
Ok, so what is the solution of a system of equations?Answer
The solution is where the equations 'meet' or intersect. The red point is the solution of the system.
How many solutions can systems of linear equations have?Answer
There can be zero solutions, 1 solution or infinite solutions--each case is explained in detail below. Note: Although systems of linear equations can have 3 or more equations,we are going to refer to the most common case--a stem with exactly 2 lines.
This is the most common situation and it involves lines that intersect exactly 1 time.
Example of a stem that has no solution:
- Line 1: y = 5x +13
- Line 2: y = 5x + 12
This is the rarest case and only occurs when you have the same line
Consider, for instance, the two lines below (y = 2x+1 and 2y = 4x +2). These two equations are really the same line .
Example of a system that has infinite solutions:
- Line 1: y = 2x + 1
- Line 2: 2y = 4x + 2
The solution of the system of equations on the left is (2,2) which marks the point where the two lines intersect.
How can we find solutions to systems of equations?
on Solutions of Systems of Equations