Chapter 5.1

Any equation of the form:
a1x1+....+anxn=b
for all real numbers a1,a2,...,an(not all of which are 0) and b, is a linear equation or a first degree equation in n unknowns

set of equations; the solutions of a system of equations must satisfy every equation in the system. If all the equations in a system are linear, the system is a system of linear equations, or a linear system

-the graphs of two equations intersect a single point
-the coordinates of this point give the only solution of the system

-the graphs are distinct parallel lines
-the equations are independent, that is, there is no solution common to both equations

-the graphs are the same line
-any solution of one equation is also the solution of the other. Thus there are infinite number of solutions.

In a system of two equation with two variables, the substitution method involves using one variable in terms of the other, then substituting into the other equation of the system.

It uses multiplication and addition to eliminate a variable from one equation. To eliminate a variable, the coefficients of that variable in the two equations must be additive inverses. To achieve this, we use properties of algebra to change the system to an equivalent system, one with the same solution set.