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7 Cards in this Set
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Linear Systems

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 

systems of equations

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


what is consistent?

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

what is inconsistent?

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

what is dependednt?

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. 

Substitution method

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.


elimination method

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.
