6.2 Solving Systems Using Substitution

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# 6.2 Solving Systems Using Substitution - PowerPoint PPT Presentation

6.2 Solving Systems Using Substitution. Standard: SWBAT solve a system of two linear equations in two variables algebraically. Mini Quiz 50. Is (4, 0) a solution of the system of equations? 2x + y = 8 -x + 3y = 4 Solve the System of Equation by graphing: 2y = 4x -y = -2x.

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## 6.2 Solving Systems Using Substitution

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### 6.2 Solving Systems Using Substitution

Standard: SWBAT solve a system of two linear equations in two variables algebraically.

Mini Quiz 50
• Is (4, 0) a solution of the system of equations? 2x + y = 8
• -x + 3y = 4
• Solve the System of Equation by graphing:
• 2y = 4x
• -y = -2x
Quick Review
• Solve the equation for x: 2y + x =12
• x = -2y + 12
• How does the graph look when there is “no solution”?
• The lines are parallel and never intersect.
• How does the graph look when there are “infinitely many solutions”?
• The two lines are the same line.
Solving by Substitution
• Pick an equation (that’s easiest to get one of the variables by itself) and solve for a variable
• Substitute into the OTHER equation
• Solve for the first variable
• Substitute and solve for the second variable (doesn’t matter which equation)

Pick Equation

• Substitute
• Solve
• Substitute and Solve
• Check
Solving by Substitution

1. Solve the linear system

-x + y = 4

-8x + 2y = 2

-x + y = 4

+x +x

y = x + 4

Check ( 1, 5)

-x + y = 4

-1 + 5 = 4

4 = 4 

-8x + 2y = 2

-8(1) + 2(5) = 2

-8 + 10 = 2

2 = 2 

-8x + 2(x + 4) = 2

-8x + 2x + 8 = 2

-6x + 8 = 2

-6x = -6

x = 1

-x + y = 4

-(1) + y = 4

y = 5

(1, 5)

Pick Equation

• Substitute
• Solve
• Substitute and Solve
• Check
Substitution

Solve the linear system

2. y = 2x – 4

x = y + 3

3. –m + n = 1

2m + n = -2

4. 2c + 2d = 3

c – 4d = -1

( 1, -2)

(-1, 0)

(1, ½)

Application

5. Your school must transport 193 people to a competition. There are eight drivers available and two types of vehicles. The school buses seat 51 people each, and the minivans seat 8 people each. How many buses and minivans will be needed?

b = number of school buses

m = number of mini vans

b + m = 8

51b + 8m = 193

(3, 5)

Substitution – No solution/Infinite solutions

6. y = 3x + 2

6x – 2y = -4

7. y = 2x + 6

4x – 2y = 8

8. 2x + y = -1

-6x – 3y = -15

9. 15x – 5y = -20

-3x + y = 4

Infinite Solution

No Solutions

No Solutions

Infinite Solution

Wrap Up

Substitution Method

• Pick an equation
• Substitute
• Solve
• Substitute and solve
• Check

No Solution

x and y cancels and two sides are different

Infinitely Many Solutions

x and y cancels and both sides are equal

HW: P. 284 # 1-5 odd, 9-17 odd; P. 286 #45-47 all

DLUQ: What happens to the variables when you have “no solution” or “infinitely many solutions”?