1. Activating Prior Knowledge – Simplify each expression.
3x + 4y – 3x – 2y (x – y) - 3x + 5y
3. 2y + 6x – 3(y + 2x) 4. 2y – 4x – 2(2y – 2x) 2y 2y -y
–2y
Tie to LO

2. Today, we will solve systems of linear equations by elimination.
Learning Objective
Today, we will solve systems of linear equations by elimination.
CFU

3. Skill Development – Notes #1
-x + y = -1
Solve by elimination.
2x - y = 0
Step 1
-x + y = -1
Write the system so that like terms are aligned.
Step 2
2x - y = 0
Add the equations to eliminate the y-terms.
x = -1
Step 3
x = -1
Simplify and solve for x.
CFU

4. Skill Development – Cont. Notes #1
Step 4
-x + y = –1
Write one of the original equations.
-(-1) + y = –1
Substitute -1 for x.
1 + y = –1 –1
y = –2
Step 5 (-1, –2)
Write the solution as an ordered pair.
CFU

5. Concept Development – Notes #2 & 3
2. When two equations each contain the same term, you can subtract one equation from the other to solve the system.
3. To subtract an equation add the opposite of each term.
CFU

6. Skill Development – Notes #4
2x + y = –5
Solve by elimination.
2x – 5y = 13
Step 1
2x + y = –5 –
(2x – 5y = 13)
Step 2
Add the opposite of each term in the second equation.
2x + y = –5
–2x + 5y = –13
Step 3
0 + 6y = –18
Eliminate the x term.
6y = –18
Simplify and solve for y.
y = –3
CFU

7. Skill Development – Cont. Notes #4
Write one of the original equations.
Step 4
2x + y = –5
2x + (–3) = –5
Substitute –3 for y.
2x – 3 = –5
Add 3 to both sides.
2x = –2
Simplify and solve for x.
x = –1
Step 5
(–1, –3)
Write the solution as an ordered pair.
CFU

8. Concept Development – Notes #5
5. In some cases, you will first need to multiply one or both of the equations by a number so that one variable has opposite coefficients.
CFU

9. Skill Development – Notes #6
Solve the system by elimination.
x + 2y = 11
–3x + y = –5
Step 1
x + 2y = 11
Multiply each term in the second equation by –2 to get opposite y-coefficients.
(–3x + y = –5) –2
Step 2
x + 2y = 11
+(6x –2y = +10)
Add the new equation to the first equation.
Step 3
7x = 21
7x = 21
x = 3
Simplify and solve for x.
CFU

10. Skill Development – Cont. Notes #6
Write one of the original equations.
Step 4
x + 2y = 11
3 + 2y = 11
Substitute 3 for x.
– –3
2y = 8
Subtract 3 from each side.
Simplify and solve for y.
y = 4
Step 5
(3, 4)
Write the solution as an ordered pair.
CFU

11. Closure – CFU 1. What did we learn today?
2. Why is this important to you?
3. What does it mean to eliminate in a systems of linear equations?
4. Solve each system by elimination.
2x + 3y = 12
5x - y = 13
(3, 2)
CFU