Systems of equations - Home
Solving Linear Systems by Substitution
Reteach
|You can use substitution to solve a system of equations if one of the equations is already solved for a variable. |
|Solve [pic] |
|Step 1: Choose the equation to use as the substitute. |Step 3: Now substitute x ’ 2 back into |
|Use the first equation y ’ x + 2 because it is already solved for a |one of the original equations to find the value of y. |
|variable. |y ’ x + 2 |
|Step 2: Solve by substitution. |y ’ 2 + 2 |
| |y ’ 4 |
| |The solution is (2, 4). |
|3x + y ’ 10 |Check: |
|3x + (x + 2) ’ 10 Substitute x + 2 for y. |Substitute (2, 4) into both equations. |
|4x + 2 ’ 10 Combine like terms. |y ’ x + 2 3x + y ’ 10 |
|[pic] |4 [pic] 2 + 2 3(2) + 4 [pic] 10 |
| |4 [pic] 4 ( 6 + 4 [pic] 10 |
| |10 [pic] 10 ( |
|You may need to solve one of the equations for a variable before solving with substitution. |
Solve each system by substitution.
1. [pic] 2. [pic]
3. [pic] 4. [pic]
LESSON 10-1 Reteach
1. 1
2. 0
3. −1
LESSON 10-2 Reteach
1. Positive
2. Possible answer: (4, 8) and (6, 11);
m ’ [pic]
3. [pic]
LESSON 11-1 Reteach
1. (−3, 2)
[pic]
2. (−4, −2)
[pic]
3. (2, 0)
[pic]
4. (3, 2)
[pic]
LESSON 11-2 Reteach
1. (7, 9)
2. (17, 7)
3. (3, 6)
4. (−1, 7)
LESSON 11-3 Reteach
1. (−6, 17)
2. (4, −1)
3. (−6, 18)
4. (2, −3)
LESSON 11-4 Reteach
1. (1, −1)
2. (−4, −14)
3. (1, 4)
4. (1, 5)
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lesson
11-2
x + 2
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