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:
- no intersection point
- 1 intersection point
- 2 intersection points
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
Exercises:
1. Solve algebraically:
2. Solve algebraically:
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.
4. Find the intersection points for the circles
and
Didn't find what you are looking for on this page? Try search:
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Algebra Lessons on DVD
Easy to understand algebra lessons on DVD. See samples before you commit.
More info: Algebra videos
Book mark this page
Add this page to Del.icio.us, Furl, Digg, StumbleUpon, Google, whatever...
Need a break? Play a math game. Well, they all involve math... No, really!






