6. Algebraic Solution of Systems of Equations


Solution by Substitution

Similar to the linear case in the previous section, we can substitute one of the expressions given into the other expression:

 

Example:

Solve the system of equations algebraically:

y = x + 1

x2 + y2 = 25

We recognise that this is a straight line intersecting a circle. We may have:


Answer


Solution by Addition or Subtraction

This method works by eliminating one of the variables from the equations. We then find the value(s) of the remaining variable.

 

Example:

Solve the system of equations by adding or subtracting

x2 + y = 5

x2 + y2 = 25


Answer


Exercises:

1. Solve algebraically:

math expression


Answer


2. Solve algebraically:

math expression


Answer


3. The impedance Z in an alternating-current circuit is 2.00 W. If the resistance R is numerically equal to the square of the reactance X, find R and X.


Answer


4. Find the intersection points for the circles

MATH

and

MATH


Answer




get MathTutorDVDs

Easy to understand math lessons on DVD. Try before you commit.
MathTutorDVD.com


Book mark this page in Del.icio.us, Furl, Digg, StumbleUpon, whatever...


Didn't find what you are looking for? Try search:


Need a break? Play a math game. Well, they all involve math... No, really!

dumbolf memoTST bola shadow factory mindfields trick-hoops-challenge crystal clear