This week we started on our 9th unit of the year, which is the systems of linear equations. Since we just started, let’s just go over the basics.
What are systems of linear equations?
Systems of linear equations are 2 lines that are complete when 2 numbers are placed into the variable spot and makes the equation true. These can also be called solutions, and are a set of numbers that make the sentence/equation true. There are 3 main kinds of systems that can be used for different kinds of lines.
What are the 3 main kinds of systems?
- The first one is for a line with different slopes, which means in this case that the slope of m1 does not equal to the slope of m2. This kind of system only has 1 solution, and these lines cross the y-axis at a set point.
- The second system is for a line that has the same slopes. There are infinite solutions, and these are called coincident lines, which mean that they overlap and are on the same lines.
- The last main kind is for parallel lines. These lines will never cross eachother on the Cartesian Plane, and because of that, do not have the same solution. They do have the same slope, so m1=m2. However, they do not have the same y-intercept, and b1 does not equal b2.
