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5.3b Solving Linear Systems of Equations
Elimination Method
Addition/Subtraction
w/ Multiplication
Can we solve both of these systems with elimination?
x - 3y = -4
x + 4y = 20
-x - 2y = -1
2x - y = 16
x + 4y = 20
2x - y = 16
Solving Systems by Elimination
1.
Rewrite system to align like terms
2.
Multiply one (or both) equation(s) so that
one of the variables can be eliminated
3.
Eliminate 1 of the variables
4.
Solve for other variable
5.
Plug it back into original equation
Solving Systems by Elimination
Example #1
x + 4y = 20
2x - y = 4
1.
Rewrite system to align like terms
2.
Multiply one (or both) equation(s) so that
one of the variables can be eliminated
x + 4y = 20
4(2x - y = 4)
x + 4y = 20
8x - 4y = 16
3.
Eliminate 1 of the variables
9x = 36
4.
Solve for other variable
x=4
5.
Plug it back into original equation
x + 4y = 20
4 + 4y = 20
4y = 16
y=4
6.
Check
1. Rewrite to align like terms
Example # 2:
4x + y = 8
x - 7y = 2
2. Multiply
3. Eliminate a variable
4. Solve
5. Plug it in
6. Check
1. Rewrite to align like terms
Example # 3:
2x + 5y = 3
-x + 3y = -7
2. Multiply
3. Eliminate a variable
4. Solve
5. Plug it in
6. Check
1. Rewrite to align like terms
Example # 4:
5x + 3y = 2
2x = -y
2. Multiply
3. Eliminate a variable
4. Solve
5. Plug it in
6. Check
1. Rewrite to align like terms
Example # 5:
5x + 3y = 12
4x - 5y = 17
2. Multiply
3. Eliminate a variable
4. Solve
5. Plug it in
6. Check
1. Rewrite to align like terms
Example # 6:
5x + 3y = -10
3x + 5y = -6
2. Multiply
3. Eliminate a variable
4. Solve
5. Plug it in
6. Check
1. Rewrite to align like terms
Example # 7:
5x + 3y = -10
3x + 5y = -6
2. Multiply
3. Eliminate a variable
4. Solve
5. Plug it in
6. Check
1. Rewrite to align like terms
Example # 7:
5x + 3y = -10
3x + 5y = -6
2. Multiply
3. Eliminate a variable
4. Solve
5. Plug it in
6. Check
7.3 Solving Linear Systems of Equations
Take 3: Elimination Method
Addition/Subtraction
w/ Multiplication
Can we solve both of these systems with elimination?
x - 3y = -4
x + 4y = 20
-x - 2y = -1
2x - y = 16
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