College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter7: Conic Sections And Quadratic Systems
Section7.4: Solving Nonlinear Systems Of Equations
Problem 62E
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Solving Linear Systems in Three Variables by Eliminating Variables
1. Reduce the system to two equations in two variables. This is usually
accomplished by taking two different pairs of equations and using the
addition method to eliminate the same variable from both pairs.
2. Solve the resulting system of two equations in two variables using addition
or substitution. The result is an equation in one variable that gives the value
of that variable.
3. Back-substitute the value of the variable found in step 2 into either of the
equations in two variables to find the value of the second variable.
4. Use the values of the two variables from steps 2 and3 to find the value of
the third variable by back-substituting into one of the original equations.
5. Check the proposed solution in each of the original equations.
Transcribed Image Text:Solving Linear Systems in Three Variables by Eliminating Variables 1. Reduce the system to two equations in two variables. This is usually accomplished by taking two different pairs of equations and using the addition method to eliminate the same variable from both pairs. 2. Solve the resulting system of two equations in two variables using addition or substitution. The result is an equation in one variable that gives the value of that variable. 3. Back-substitute the value of the variable found in step 2 into either of the equations in two variables to find the value of the second variable. 4. Use the values of the two variables from steps 2 and3 to find the value of the third variable by back-substituting into one of the original equations. 5. Check the proposed solution in each of the original equations.
9:274
(5 <xS 15
y 22
(x +y < 20
4) Consider the linear system defined by
a. Graph the system using technology. Be sure to edit each axis range to get a clear picture of
the solution region. Label the solution region etc.
b. Choose a test point and show algebraically that it IS a solution. Add the labeled point to
your graph.
C. Write a statement that explains your test point (x, y) in part b is a solution.
d. Choose a test point and show algebraically that it IS NOT a solution. Add the labeled point
to your graph.
e. Write a statement that explains your particular solution (x, y) in part d.
Note: Some graphing tips can be found in the "Refer to the Course Specific Information Module
on the "Technology Tools" page and "Online Graphing Tools tab" for graphing help.
Transcribed Image Text:9:274 (5 <xS 15 y 22 (x +y < 20 4) Consider the linear system defined by a. Graph the system using technology. Be sure to edit each axis range to get a clear picture of the solution region. Label the solution region etc. b. Choose a test point and show algebraically that it IS a solution. Add the labeled point to your graph. C. Write a statement that explains your test point (x, y) in part b is a solution. d. Choose a test point and show algebraically that it IS NOT a solution. Add the labeled point to your graph. e. Write a statement that explains your particular solution (x, y) in part d. Note: Some graphing tips can be found in the "Refer to the Course Specific Information Module on the "Technology Tools" page and "Online Graphing Tools tab" for graphing help.
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