Chapter 1: linear systems
by namya m
1. the linear equations may have different number of variables. however, the number of equations required to obtain the value of all the variables are equal to the total number of variables present
2. the equations with the highest degree 1 are known as linear equations. when there are more than one linear equations, it is known as a linear system
3. linear systems can be drawn on a coordinate plane in the form of a line- by either knowing the slope of the line and one point on the line or by knowing at least two points on the line
4. linear systems with two variables may have a unique solution, infinitely many solutions or no solutions. the solution for a system of linear equations can be found by many methods.
4.1. SOLVING BY SUBSTITUTION: a linear system can be solved by substituting the value of one variable in the first equation into the second equation
4.2. BY GRAPHING: by t-tables, slope intercept form, and the x and y intercepts
4.3. BY ELIMINATION: solutions can be obtained by making one of the variables' constant in one of the equations equal to the that in the second and then adding or subtracting the equations. after that the values can be substituted in order to obtain the value of the other variable
4.4. BY CROSS MULTIPLICATION: the constants and the coefficients are cross multiplied to obtain the results for the variables
