Download 7.3- Solving Linear Systems by Linear Combinations

7.3- Solving Linear Systems by
Linear Combinations
Objective:
• Use linear combinations to solve a system of
linear equations
Vocabulary
Linear Combination- of two equations is
an equation obtained by adding one of the
equations to the other equation.
Solving Linear Systems by Linear
Combinations

This is the third and final way to solve
linear systems.

graphing
The other two are ____________
and
substitution
______________.

Sometimes it is not easy to isolate one of
the variables, so you would use linear
combinations
Steps
Arrange the equations with like terms in
columns.
2) Multiply one or both equations by a
number to obtain coefficients that are
opposites for one variable.
3) Add the equations from Step 2. One
variable will be eliminated. Solve for the
other.
4) Substitute this number into either original
equation and solve for the other variable.
5) Check.
1)
Solve
Step 4
Step 1
-2x + 2y = -8
2x + 6y = -16
8y = -24
Step 3
y = -3
Step 5
2x + 6y = -16
2x + 6(-3) = -16
2x – 18 = -16
2x = 2
x=1
Solution: (1, -3)
Check: -2(1) + 2(-3) = -8
2(1) + 6(-3) = -16
Solve
3x = -6y + 12
-x + 3y = 6
Rewrite the top:
3x + 6y = 12
[ -x + 3y = 6 ]3
-3x + 9y = 18
15y = 30
y=2
-x + 3y = 6
-x + 3(2) = 6
-x + 6 = 6
-x = 0
x=0
Solution: (0, 2)
Check: 3(0) = -6(2) + 12
-(0) + 3(2) = 6
You try! Solve.
2x + 8y = -2
[ 5x + 4y = 3 ]-2
-10x - 8y = -6
-8x
= -8
x=1
2(1) + 8y = -2
2 + 8y = -2
8y = -4
y = -½
Answer: (1, -½)
Check: 2(1) + 8(-½) = -2
5(1) + 4(-½) = 3
Assignment
7.3- (pg. 414-415)
# 8-38 EVEN