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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
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.
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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