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Aim #24: How do we solve a system of linear equations algebraically using
elimination?
Homework: Handout
Do Now:
a) What is the additive inverse of 4? _____
b) What is the additive inverse of -7x? _____
To solve algebraically by using elimination, our goal is to make one of the variables
cancel out when we add or subtract the two linear equations.
Solve the following system by eliminating the x - variable.
2x + 3y = 7
x-y=1
Solve the following system by eliminating the y - variable.
2x + 3y = 7
x-y=1
What property allows us to solve a system of equations using elimination without
changing the solution set?
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Solve the following systems of equations using elimination.
1) x - 2y = 1
-4y = -7 + x
2)
y = 5x - 1
2y = 3x + 12
.
3) 2x + 3y = 21
5x - 2y = -14
4)
5
x
2
= 2y +
3
2
3y = x -
15
2
9
2
4
5)
2x + 3y = 5
6y = -4x + 10
6)
2x -
y =
x + 4y = 5
7)
4x - 8y = 15
-5x + 10y = -30
8)
x - 2y = 3
3x - y = 2
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9) 9x + y = 51
7x +
y = 39
10) x + 4y = 8
-16y = 4x - 32
Let's sum it up!!!
To solve a system of linear equations by elimination:
• Rearrange the equations so that the like terms are on top of each other.
• If two terms are exactly the same but with different signs, just add down.
• If two terms are exactly the same and have the same sign, multiply one
row by -1.
• Solve the new equation.
• Plug in the value of the variable into one of the original equations to find
the other variable.
• Check your solution!
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