3.2 Solving Linear Systems Algebraically

1
3.2 Solving Linear Systems Algebraically
2
Objectives/Assignment

• Use algebraic methods to solve linear systems.
• Assignment 11-53 odd

3
Warm-Up
y 2x-5
x 3 2y
y (3/4)x -3
x 4 (4/3)y
4
The Substitution Method
x -2y 2
Solve this equation for x
Substitute -2y 2 for x in the first equation.
3x 4y -4
-6y64y -4
3(-2y2)4y -4
Finally, substitute 5 for y (in x -2y 2) and
solve for x.
y 5
x -8
(-8,5) is the solution to the system.
5
The Substitution Method
Check the ordered pair (-8,5) by substituting it
into each equation to verify it is really the
solution.
y 5
x -8
(-8,5) is the solution to the system.
6
The Linear Combination Method Multiplying One
Equation
Multiply the first equation by -2
-2
Add the equations together
3y -18
y -6
Use this value for y and substitute it into
either of the equations. Solve for x.
The ordered pair (-11/2,-6) is the solution to
this system
x-(11/2)
4x 5(-6) 8
7
The Linear Combination Method Multiplying One
Equation
Multiply the first equation by -2
-2
3y -18
Why Choose the multiplier -2??
y -6
The ordered pair (-11/2,-6) is the solution to
this system
x-(11/2)
8
(1/2,4)
9
Solve the system using the Linear Combination
Method.
(-1,5)
10
What about these??

• a. x-2y3 b. 6x-10y12
• 2x-4y7 -15x25y-30