Recall that a system of equations is two or more equations
considered together. (See Section 5.1.)
In particular, if all of those functions are linear , we call it a _______
___________ of ____________.
We studied the Method .html">Substitution Method in Section 5.1. Now we will learn the
_____________ Method.
Solving by Elimination :
1. Arrange the equations so that they have the same form – the variables are
lined up
2. Multiply one or both equations by constants so that x or y has the same
coefficient (or)
different signs
3. Add the equations . One variable is eliminated . Solve for the remaining
variable.
4. Back-substitute in one of the equations and solve for the other variable
Example 1: Solve the fol lowing systems of equations.
Recall that a _________ of a system of equations is an
________ ______ that is a solution of _____
equations.
Ex.
Example 2: Solve
Let us see the above example again. We notice that the
equation (2) divides 2 gives us the equation
(1). This is the case of a dependent system of equations. If you notice a system
of equations is
dependent, there is a simpler method for solving it. Let us try Example 2 again.
Example 2’: Solve
Example 3: De termine which system of equations are
dependent.
Let us see Example 3, e. one more time. Notice that the
left-hand side of the second equation is
obtained as three times the left-hand side of the first equations. But this is
not a dependent system of
equations, because the constant term cannot be obtained in the same way. This is
the case of
inconsistent.
Example 4: Solve
Graphically :
Example 5: Solve:
