Chapter 4.1, Problem 18E

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# In Exercises 7-20, find all solutions of the given system of equations, and check your answer graphically.[HINT: See Examples 2-5.] 2 x − 3 y = 1 6 x − 9 y = 3

To determine

To calculate: The solution to the system of equations 2x3y=1 and 6x9y=3 and check the answer graphically.

Explanation

Given Information:

The provided system of equations is,

2xā3y=16xā9y=3

Formula used:

Elimination Method:

This method is used to find the solutions of the system of linear equations by eliminating one of the two variables from the equations.

Multiply the equations with suitable non-zero numbers. Then combine the equations in such a way so that one of the variables get eliminated and then evaluate the value of the other variable. Then substitute the value of this variable in either of the equations to get the value of the first variable.

Calculation:

Consider the equations,

2xā3y=1 ā¦ā¦ (1)

6xā9y=3 ā¦ā¦ (2)

Multiply equation (1) by 3 and equation (2) by ā1.

3ā(2xā3y)=3(1)6xā9y=3

And

ā1ā(6xā9y)=ā1(3)ā6x+9y=ā3

Ā Ā 6xā9y=3ā6x+9y=ā3_Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā 0=0Ā

It seems that the provided system of equations has infinite solutions.

To find the solution of the system of equations, graphically, plot the graphs of the equations and find the intersection point.

To plot the graph of the equations, find the ordered pairs.

Consider the equation, 2xā3y=1Ā

Substitute x=0 in the equation 2xā3y=1.

2(0)ā3y=10ā3y=1ā3y=1y=ā13

Substitute x=12 in the equation 2xā3y=1.

2(12)ā3y=11ā3y=1ā3y=1ā1ā3y=0

Simplify it further,

y=0

Substitute x=ā1 in the equation 2xā3y=1

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