Download 7.2A Solving systems with elimination

Precalculus
7.2 Systems of Linear Equations in Two Variables
Method of Elimination:
1.
2.
3.
4.
Obtain coefficients for x (or y) that differ only in sign by multiplying all terms of one or
both equations by suitably chosen constants.
Add the equations to eliminate one variable and solve the resulting equation.
Back-substitute the value obtained in step 2 into either of the original equations and solve
for the other variable.
Check your solution in both of the original equations.
Graphical Interpretation of Solutions
For a system of two linear equations in two variables, the number of solutions is one of the
following.
1.
2.
3.
Number of Solutions
Exactly One Solution
Infinitely Many Solutions
No Solution
Graphical Interpretation
The two lines intersect at one point.
The two lines are coincident (identical).
The two lines are parallel.
Example #1:
Solve the following system of linear equations.
3x  2 y  4
5x  2 y  8
Example #2:
Solve the following system of linear equations.
2 x  3 y  7
3 x  y  5
Example #3:
Solve the following system of linear equations.
5x  3 y  9
2 x  4 y  14
Example #4:
Solve the following system of linear equations.
x  2y  3
 2x  4 y  1
Example #5:
Solve the following system of linear equations.
2x  y  1
4x  2 y  2
Example #6:
Solve the following system of linear equations.
0.02 x  0.05 y  0.38
0.03x  0.04 y  1.04
Example #7:
An airplane flying into a headwind travels the 2000-mile flying distance between two cities in 4
hours and 24 minutes. On the return flight, the same distance is traveled in 4 hours. Find the
ground speed of the plane and the speed of the wind, assuming that both remain constant.
Example #8:
Suppose the demand and supply functions for a certain type of calculator are given by
p  150  10 x
p  60  20 x
where p is the price in dollars and x represents the number of units in millions. Find the point of
equilibrium for this market by solving this system of equations. (The point of equilibrium is the
price p and the number of units x that satisfy both the demand and the supply equations.)
Assignment 7-2A Pages 491 #2-16 even, 22-36 even, 42-52 even, 68-78 even