Download Lesson 1: 2 Equations 2 Unknowns

SYSTEMS OF
EQUATIONS
Internal 3 credits
Note 1: Systems of Equations
Systems of equations involve two or more variables
related to each other through a set of equations.
The solution to the system is the set of values of the
variables which satisfies all equations.
Algebraic methods used to solve are:
 Elimination
 Substitution
Note 2: 2 Equations 2 Unknowns
Elimination
Both equations need to be in the same format
Example: Solve y – 3x = 5
(1)
2y – x = 5
(2)
Multiply equation (1) by -2 to eliminate y:
-2y + 6x = -10
(1)
2y – x = 5
(2)
5x = -5
x = -1
Substitute result into either of the two equations
y – 3 × -1 = 5
y+3=5
y=2
Therefore the solution is (-1, 2)
Substitution
One of the equations must be in the form y = or x =
Example: Solve y – 3x = 5
(1)
2y – x = 5
(2)
Rearrange equation (1)
y = 3x + 5
(1)
2y – x = 5
(2)
Replace y in equation (2) with 3x + 5 and solve for x
2(3x + 5) – x = 5
6x + 10 – x = 5
5x + 10 = 5
5x = -5
x = -1
Substitute result into equation (1)
y = 3 × -1 + 5
y=2
Therefore the solution is (-1, 2)
Page 199
Exercise A