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





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