Task 3 (a) Write down what a system of two linear equations in two unknowns would look like in Cramer's notation. Solve the pair of equations by multiplying each equation by a quantity that allows for the elimination of the variable y when the equations are subtracted one from the other; this reduces the two equations to a single equation in 2. Solve for z in terms of the coefficients of the system. Now use a similar procedure (multiplying each of the original equations by a quantity that allows for the elimination of the variable : when the equations are subtracted) to solve for y. Compare your formulas with those of Cramer. (b) Use Cramer's Rule to solve the system 4 = 7: + 10y 3 = 5: + 7y (c) Discuss what happens when you use Cramer's Rule to solve the system 10 = - 3y -1 = 4: - 12y
Task 3 (a) Write down what a system of two linear equations in two unknowns would look like in Cramer's notation. Solve the pair of equations by multiplying each equation by a quantity that allows for the elimination of the variable y when the equations are subtracted one from the other; this reduces the two equations to a single equation in 2. Solve for z in terms of the coefficients of the system. Now use a similar procedure (multiplying each of the original equations by a quantity that allows for the elimination of the variable : when the equations are subtracted) to solve for y. Compare your formulas with those of Cramer. (b) Use Cramer's Rule to solve the system 4 = 7: + 10y 3 = 5: + 7y (c) Discuss what happens when you use Cramer's Rule to solve the system 10 = - 3y -1 = 4: - 12y
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter5: Systems Of Linear Equations
Section5.4: Solve Applications With Systems Of Equations
Problem 5.85TI: Translate to a system of equations and then solve: A Mississippi river boat cruise sailed 120 miles...
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Question
Task 3
![Task 3 (a) Write down what a system of two linear equations in two unknowns would look like in
Cramer's notation. Solve the pair of equations by multiplying each equation by a quantity
that allows for the elimination of the variable y when the equations are subtracted one
from the other; this reduces the two equations to a single equation in z. Solve for z in
terms of the coefficients of the system. Now use a similar procedure (multiplying each
of the original equations by a quantity that allows for the elimination of the variable z
when the equations are subtracted) to solve for y. Compare your formulas with those of
Cramer.
(b) Use Cramer's Rule to solve the system
4 = 72 + 10y
3 = 5z + 7y
(c) Discuss what happens when you use Cramer's Rule to solve the system
10 = 2 – 3y
-1 = 4: - 12y
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9774f45-b264-467e-8b06-716b402d428d%2Ff5687343-069e-4099-bda9-5b7f71c4e950%2F3mydchs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Task 3 (a) Write down what a system of two linear equations in two unknowns would look like in
Cramer's notation. Solve the pair of equations by multiplying each equation by a quantity
that allows for the elimination of the variable y when the equations are subtracted one
from the other; this reduces the two equations to a single equation in z. Solve for z in
terms of the coefficients of the system. Now use a similar procedure (multiplying each
of the original equations by a quantity that allows for the elimination of the variable z
when the equations are subtracted) to solve for y. Compare your formulas with those of
Cramer.
(b) Use Cramer's Rule to solve the system
4 = 72 + 10y
3 = 5z + 7y
(c) Discuss what happens when you use Cramer's Rule to solve the system
10 = 2 – 3y
-1 = 4: - 12y
4
![(d) Try to formulate a criterion in terms of the coefficients of a linear system of two equations
in two unknowns for when it is possible to solve the system and when it is not possible.
Explain what you find in as much detail as you can.
(e) Graph the two equations in (b) in a (z, y)-coordinate plane. Relate the features of your
graph to your answer to part (b).
(f) Repeat part (e) using the equations in (c), and note what you observe.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9774f45-b264-467e-8b06-716b402d428d%2Ff5687343-069e-4099-bda9-5b7f71c4e950%2Fagbn14g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(d) Try to formulate a criterion in terms of the coefficients of a linear system of two equations
in two unknowns for when it is possible to solve the system and when it is not possible.
Explain what you find in as much detail as you can.
(e) Graph the two equations in (b) in a (z, y)-coordinate plane. Relate the features of your
graph to your answer to part (b).
(f) Repeat part (e) using the equations in (c), and note what you observe.
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