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Algebra 1
Lesson Notes 7.4A
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Review least common multiples (AKA least common denominator when we are talking about
combining fractions).
Multiply all unique prime factors of each number.
Or take multiples of one number until you get a multiple of the other number.
Try it:
6 and 10
8 and 6
12 and 4
9 and 12
Objective: Solve a system of linear equations using linear combination with multiplicaton.
Solving a system of equations using the linear combination method:
Step 1:
If necessary, rewrite the equations in standard form to arrange
like variables.
Step 2:
If necessary, multiply one of the equations by -1 so that one of
the variables has the opposite coefficient in the two equations.
OR
If necessary, multiply one or both equations so that one of the
variables has the opposite coefficient in the two equations.
Step 3.
Combine the equations to eliminate one variable.
Step 4:
Solve the resulting equation for the remaining variable.
Step 5:
Substitute the value from Step 4 into either original equation
to find the value of the eliminated variable.
Step 6:
Check your solution for accuracy.
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Example 1 (p 451): Multiply one equation, then combine
Solve the linear system.
2 x  3 y  11
5 x  14  6 y
Another Example 1 (p 451): Multiply one equation, then combine
Solve the linear system.
4 x  6 y  52
3x  2 y  34
Example 2 (p 452):
Multiply both equations, then combine
Solve the linear system.
2 x  6 y  14
9x  1  4 y
 CW: Guided Practice p 452 # 1-3
 HW: A5 pp 454-455 #3, 5, 6, 8-11*
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*Check your answers!
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Objective:
Determine the number of solutions to a system of linear equations using linear
combination.
A system of equations may have:
1 solution ↔ solving by linear combination results in values for x and y
no solution ↔ solving by linear combination results in a false statement
infinite solutions ↔ solving by linear combination results in a statement
that is always true
Example 1 (p 459): A linear system with no solution
3x  2 y  5
6x  4 y   8
Example 2 (p 460): A linear system with infinitely many solutions
4x  6 y  8
2x  3 y  4
 CW: Lesson 7-4 Practice A
 HW: A6a p 455 #12-15, p 463 #15, 17, 18, 29
A6b Lesson 7-4 Practice B / Lesson 7-5 Practice B
Prepare for Quiz 7.3-7.4
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