1. Section 7.1 “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).

2. Section 7.2 “Solve Linear Systems by Substitution”
Solving a Linear System by Substitution
(1) 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.

3. “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

4. “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

5. 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

6. 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

7. 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?
y = 2x
x =
$2.50y + $2.00x = $336
y =
96 bags of popcorn and 48 pretzels

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

9. NJASK7 prep
Homework
Text p. 439, #4-24 even, #32, #36