1. Do Now 12/11/18
Take out HW from last night.
Text p. 239, #4-22 evens, 27 & 28
Copy HW in your planner.
Text p. 245, #9-18 all, 20 & 27
GoFormative.com. Solve the system below by graphing.
x – y = 4
4x + y = 1

2. Solve the system by graphing.
x – y = x + y = 1
Section 3.4

3. Homework Text p. 239, #4-22 evens, 27 & 28

4. Learning Goal Learning Target
Students will be able to write and graph systems of linear equations.
Learning Target
Students will be able to solve systems of linear equations by substitution

5. Section 5.1 “Solve Linear Systems by Graphing”
consists of two more linear equations.
x + 2y = 7
Equation 1
3x – 2y = 5
Equation 2
A solution to a linear system is an ordered
pair (a point) where the two linear equations
(lines) intersect (cross).

6. Solve a multi-step problem
A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.
STEP 1
Write a linear system. Let x be the number of pairs of skates rented, and let y be the number of bicycles rented.
x + y =25
Equation for number of rentals
15x + 30y = 450
Equation for money collected from rentals

7. Solve a multi-step problem
Graph both equations.
STEP 3
Estimate the point of intersection. The two lines appear to intersect at (20, 5).
STEP 4
Check whether (20, 5) is a solution. = ?
15(20) + 30(5) = ?
25 = 25
450 = 450
ANSWER
The business rented 20 pairs of skates and 5 bicycles.

8. Section 5.2 “Solve Linear Systems by Substitution”
Solving a Linear System by Substitution
Solve one of the equations for one of its variables. (When possible, solve for a variable that has a coefficient of 1 or -1).
(2) Substitute the expression from step 1 into the other equation and solve for the other variable.
(3) Substitute the value from step 2 into the revised equation from step 1 and solve.

9. “Solve Linear Systems by Substituting”
y = 3x + 2
Equation 1
x + 2y = 11
Equation 2
x + 2(3x + 2) = 11
x + 2y = 11
Substitute
x + 6x + 4 = 11
7x + 4 = 11
x = 1
y = 3x + 2
Equation 1
Substitute value for
x into the original equation
y = 3(1) + 2
y = 5
(5) = 3(1) + 2
5 = 5
The solution is the point (1,5).
Substitute (1,5) into both equations to check.
(1) + 2(5) = 11
11 = 11

10. “Solve Linear Systems by Substituting”
Equation 1
x – 2y = -6
x = y
Equation 2
4x + 6y = 4
4x + 6y = 4
4(-6 + 2y) + 6y = 4
Substitute
y + 6y = 4
y = 4
y = 2
x – 2y = -6
Equation 1
Substitute value for
x into the original equation
x = (2)
x = -2
(-2) - 2(2) = -6
-6 = -6
The solution is the point (-2,2).
Substitute (-2,2) into both equations to check.
4(-2) + 6(2) = 4
4 = 4

11. Solve a multi-step problem
A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.
STEP 1
Write a linear system. Let x be the number of pairs of skates rented, and let y be the number of bicycles rented.
x + y =25
Equation for number of rentals
15x + 30y = 450
Equation for money collected from rentals

12. Solve a multi-step problem
Solve equation 1 for x.
Equation 1
x + y = 25
x = 25 - y
Equation 2
15x + 30y = 450
Substitute
15(25 - y) + 30y = 450
15x + 30y = 450
y + 30y = 450
y = 450
15y = 75
y = 5
x + y = 25
Equation 1
Substitute value for
x into the original equation
x + (5) = 25
ANSWER
The business rented 20 pairs of skates and 5 bicycles.
x = 20

13. During a football game, a bag of popcorn sells for $2
During a football game, a bag of popcorn sells for $2.50 and a pretzel sells for $ The total amount of money collected during the game was $336. Twice as many bags of popcorn sold compared to pretzels. How many bags of popcorn and pretzels were sold during the game?
$2.00x + $2.50y = $336
x =
y = 2x
y =
96 bags of popcorn and 48 pretzels

14. Guided Practice y = 2x + 5 3x + y = 10 x – y = 3 x + 2y = -6 (1, 7)
(0, -3)

15. Homework
Text p. 245, #9-18 all, 20 & 27