Download 8.4 Solve Linear Systems by Elimination Using Multiplication

8.4 Solve Linear Systems by Elimination Using Multiplication
Some systems are not easily solved by adding or subtracting the equations.
You have to multiply to create opposite coefficients (LCM) first. For example:
The opposite coefficients are +4 and -4.
In some cases, you may have to multiply BOTH equations first to create opposite
coefficients. For example:
2x – 9y = 1
x 4
7x – 12y = 23
x – 3
8x – 36y = 4
-21x + 36y = -69
The opposite coefficients are - 36 and +36.
Steps
Step 1: Multiply one or both of the equations by a constant to
create opposite coefficients.
Step 2: Add the equations to eliminate (cancel) one variable.
Step 3: Solve this equation for the remaining variable.
Step 4: Substitute in one of the original equations to find the value of
the other variable.
Step 5: Write the solution as an ordered pair.
Solve each system.
Ex 1: 3x - 3y = 21
8x + 6y = -14
Ex 2: 5y = 9x - 8
-20x + 10y = -10
Ex 3: 2 x + 3y = -34
3
x − 1 y = -1
2
Ex 4: 7x + 2y = 26
10x – 5y = -10
Methods for Solving Linear Systems
When you want to see the
intersection
Graphing
When one equation is easily solved
for x or y
Substitution
y = 4 – 2x
4x + 2y = 8
Elimination Using
Addition
4x + 7y = 15
6x – 7y = 5
When the coefficients of one
variable are opposites
Elimination Using
Subtraction
(Multiply by -1)
3x + 5y = -13
3x + 2y = -5
When the coefficients of one
variable are the same
Elimination
9x + 2y = 38
3x – 5y = 7
When no corresponding
coefficients are the same or
opposites
State the best method to use to solve the following linear systems.
Ex 5:
-2x + 5y = 14
8x + 5y = 94
Ex 6:
4x = -21 + y
-3x + 7y = 51
Ex 7:
-3x + 11y = -38
2x = -40 -9y
Ex 8:
4.5x + 0.5y = 48.5
2.5x = 0.5y + 14.5