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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.

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6 2 solving systems using substitution

6.2 Solving Systems Using Substitution

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

mini quiz 50
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
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
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)
  • Check your solution (YES, you need to check your answer!)
solving by substitution1

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)

substitution

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
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
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
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”?