Table of Contents

Solving Linear Systems of Equations - Substitution Method

• Recall that to solve the linear system of equations in two variables ... 222

111

cybxa

cybxa

we need to find the value of x and y that satisfies both equations. In this presentation the Substitution Method will be demonstrated.

• Example 1:

2yx

4yx

Solve the following system

of equations ...

Table of Contents Slide 2

Solving Linear Systems of Equations - Substitution Method

2yx

4yx

• Label the equations as

# 1 and # 2. 2#

1#

• Start with equation # 2 and solve for x ...

2yx

2yx

• Since y - 2 is the same value as x, we can substitute y - 2 for x in equation # 1 ...

4yx

4y)2y(

Table of Contents Slide 3

Solving Linear Systems of Equations - Substitution Method

4y)2y( • Solve this equation for y ...

3y • Substitute this value for y in equation # 2 and solve for x ...

2yx 23x

1x • The solution to the system is (1,3), or

x = 1 y = 3

Table of Contents Slide 4

Solving Linear Systems of Equations - Substitution Method

• Summary:

1) Solve for one variable in either equation. Choose a variable that has a coefficient of 1 if possible.

2) Substitute the expression for the variable in the other equation. This leaves one equation in one unkown, for which we can solve.

3) Substitute the given value for the variable into either equation and solve for the other variable.

4) To check the solutions, substitute both values into the equation that was not used in step 3.

Table of Contents Slide 5

Solving Linear Systems of Equations - Substitution Method

• Example 2:Solve the following system of equations ...

• Solve the second equation for y ...

3y2x7

8y4x3

2#

1#

3y2x7 3x7y2

2

3x7y

Table of Contents Slide 6

Solving Linear Systems of Equations - Substitution Method

82

3x74x3

2

3x7y

• Substitute the expression for y in equation # 1 ...

and solve for x ... 83x72x3

86x14x3 86x17

17

2x

Table of Contents Slide 7

Solving Linear Systems of Equations - Substitution Method

• Substitute the value for x into equation # 1 (either equation could be used at this point) ...

17

2x

8y4x3

8y417

23

and solve for y ... 136y686

34

65y • The solution to the system is ...

17

2x

34

65y

Table of Contents Slide 8

Solving Linear Systems of Equations - Substitution Method

334

652

17

27

• Since equation # 1 was used in the last step, check by substituting the values into equation # 2 ...

33

3y2x7

Table of Contents

Solving Linear Systems of Equations - Substitution Method