Download Chapter 8 Systems of Linear Equations in Two Variables Section 8.3

Chapter 8
Systems of Linear Equations in Two Variables
Section 8.3
Chapter 8
Systems of Linear Equations in Two Variables
Section 8.3
Exercise #19
Solve the system using the addition method.
3x – 5y = 13
x – 2y = 5
Solve the system using the addition method.
3x – 5y = 13
x – 2y = 5 – 3 x – 2y = 5


– 3x + 6y = – 15
Solve the system using the addition method.
3x – 5y = 13
x – 2y = 5 – 3 x – 2y = 5


– 3x + 6y = – 15
3x – 5y = 13
y = –2
Solve the system using the addition method.
3x – 5y = 13
x – 2y = 5 – 3 x – 2y = 5


– 3x + 6y = – 15
3x – 5y = 13
y = –2
x – 2y = 5
 
x –2 –2 =5
1, – 2
x +4=5
x =1
Chapter 8
Systems of Linear Equations in Two Variables
Section 8.3
Exercise #21
Solve the system using the addition method.
– 2x + y = – 5
8x – 4y = 12
Solve the system using the addition method.
– 2x + y = – 5
4 – 2x + y = – 5
8x – 4y = 12
– 8x + 4y = – 20


Solve the system using the addition method.
– 2x + y = – 5
4 – 2x + y = – 5
8x – 4y = 12
– 8x + 4y = – 20
8x – 4y = – 12
0 = –8

No
solution.

Chapter 8
Systems of Linear Equations in Two Variables
Section 8.3
Exercise #29
Solve the system using the addition method.
2 x + 1 = – 3y + 9
3x – 10 = – 4y
 
Solve the system using the addition method.
2 x + 1 = – 3y + 9
2x + 2 = – 3y + 9
 
2x + 3y = 7
3x – 10 = – 4y
3x + 4y = 10
Solve the system using the addition method.
2x + 3y = 7
3x + 4y = 10
Solve the system using the addition method.
3 2x + 3y = 7
6x + 9y = 21


– 2 3x + 4y = 10 
Solve the system using the addition method.
3 2x + 3y = 7
6x + 9y = 21


– 2 3x + 4y = 10 
– 6x – 8y = – 20
Solve the system using the addition method.
3 2x + 3y = 7
6x + 9y = 21


– 2 3x + 4y = 10 
– 6x – 8y = – 20
y =1
Solve the system using the addition method.
2x + 3y = 7

2x + 3 1 = 7
2x + 3 = 7
2x = 4
x =2
2, 1
Chapter 8
Systems of Linear Equations in Two Variables
Section 8.3
Exercise #53
Set up a system of linear equations, and solve
for the indicated quantities.
Eight times the smaller of two numbers
plus 2 times the larger number is 44.
Three times the smaller number
minus 2 times the larger number
is zero. Find the numbers.
x = smaller number
y = larger number
Set up a system of linear equations, and solve
for the indicated quantities.
8x + 2y = 44
3x – 2y = 0
11x = 44
x =4
x = smaller number
y = larger number
Set up a system of linear equations, and solve
for the indicated quantities.

8 4 + 2y = 44
32 + 2y = 44
2y = 12
y =6
The numbers are 4 and 6.
Chapter 8
Systems of Linear Equations in Two Variables
Section 8.3
Exercise #55
Set up a system of linear equations, and solve
for the indicated quantities.
The number of calories in a piece of cake is
20 less than 3 times the number of calories
in a scoop of ice cream. Together, the
cake and ice cream have 460 Calories.
How many calories are in each?
x = number of calories
in a piece of cake
y = number of calories in
a scoop of ice cream
Set up a system of linear equations, and solve
for the indicated quantities.
x = 3y – 20
x + y = 460
x = number of calories
in a piece of cake
y = number of calories in
a scoop of ice cream
Set up a system of linear equations, and solve
for the indicated quantities.
x – 3y = – 20
x + y = 460
Set up a system of linear equations, and solve
for the indicated quantities.
– 1 x – 3y = – 20
– x + 3y = 20
x + y = 460


Set up a system of linear equations, and solve
for the indicated quantities.
– 1 x – 3y = – 20
– x + 3y = 20
x + y = 460
x + y = 460


Set up a system of linear equations, and solve
for the indicated quantities.
– 1 x – 3y = – 20
– x + 3y = 20
x + y = 460
x + y = 460
4y = 480


y = 120
x = 3y – 20
Set up a system of linear equations, and solve
for the indicated quantities.
– 1 x – 3y = – 20
– x + 3y = 20
x + y = 460
x + y = 460
4y = 480


 
y = 120
x = 3 120 – 20
x = 360 – 20
x = 340
The cake has 340 calories, and
the ice cream has 120 calories.