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SolvingSystems of Equations by Substitution and Addition

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Solving by Substitution
Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent.

36.)
y= - 3x + 19
y= 2x -1

38.)
Y= -4x -7
Y= 3x

42.)
Y= x + 4
3y -5x =6

56.)
2x -y =4
2x -y =3

Solve each system by the substitution method.

70.)
X + 3y= 2
-x + y = 1

Section 7.2: Exercises 8, 12, 16, 22, 26, 36, and 44
The Addition Method
Solve each system by addition.

8.)
X + y = 7
X - y = 9

12.)
X - 2y = -1
-x + 5y = 4

16.)
3x + 5y = - 11
X - 2y = 3

22.)
2x = 2 -y
3x + y = -1

Solve each system by the addition method. Determine whether
the equations are independent, dependent, or inconsistent.

26.)
X - y = 3
-6x + 6y = 17

Equations Involving Fractions or Decimals
Solve each system by the addition method.

36.)
3x + 5y = 27
7 9

44.)
3x - 2.5y = 7.125
2.5x - 3y = 7.3125

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Section 7.1: Exercises 36, 38, 42, 56, and 70

Solving by Substitution
Solve each system by substitution. Determine whether the
equations are independent, dependent, or inconsistent.

36.)
y= - 3x + 19
y= 2x -1

Replace by value of y in second equation by y in first equation, we will get
2x - 1 = -3x + 19
Bring all the variables to left side and numbers to right side, we will get
5x = 20
x = 4
Substitute value of x in y = 2x - 1
y = 2*4 - 1 = 8 - 1 = 7
The solution is x = 4, y = 7
The system is independent.
38.)
Y= -4x -7
Y= 3x
Replace by value of y in second equation by y in first equation, we will get
3x = -4x - 7
Bring all the variables to left side and numbers to right side, we will get
7x = -7
X = -1
Substitute value of x in y = 3x, we will get
y = 3x = 3(-1) = -3
The solution is x = -1, y = -3
The system is ...

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