Answer ( x , y ) = ( 1 , 3 ) Explanation Given: Equations: 2 x + 5 y = 17 x − 2 y = − 5 Concept used: The following steps are to be followed to find the unique solution to the system of equations: Choose an equation to find same coefficient in the equations. If the system of equations does not have same coefficient, multiply either one or both the equations with a common factor. Add or subtract the equations to find the value of one of the variables. Substitute the variable found in any of the equations and find the other which is the unique solution. Calculation: Consider the given equations. 2 x + 5 y = 17 ................... ( i ) x − 2 y = − 5 .................... ( i i ) Multiply ( i i ) with 2, 2 x − 4 y = − 10................ ( i i i ) Subtract equations ( ii ) from ( iii ), ⇒ ( 2 x + 5 y ) − ( 2 x − 4 y ) = 17 − ( − 10 ) ⇒ 2 x + 5 y − 2 x + 4 y = 17 + 10 ⇒ 5 y + 4 y = 17 + 10 ⇒ 9 y = 27 ⇒ 9 y 9 = 27 9 ⇒ y = 3 Substituting y = 3 in ( ii ), ⇒ x − 2 y = − 5 ⇒ x − 2 ( 3 ) = − 5 ⇒ x − 6 = − 5 ⇒ x − 6 + 6 = − 5 + 6 ⇒ x = 1 Conclusion: Therefore, the unique solution to the equation is ( x , y ) = ( 1 , 3 ) .

Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.7, Problem 11MRE

To determine

To find a unique solution of the system of equations.

Expert Solution & Answer

Answer to Problem 11MRE

(x,y)=(1,3)

Explanation of Solution

Given:

Equations:

2x+5y=17x−2y=−5

Concept used:

The following steps are to be followed to find the unique solution to the system of equations:

Choose an equation to find same coefficient in the equations.
If the system of equations does not have same coefficient, multiply either one or both the equations with a common factor.
Add or subtract the equations to find the value of one of the variables.
Substitute the variable found in any of the equations and find the other which is the unique solution.

Calculation:

Consider the given equations.

2x+5y=17 ...................(i)x−2y=−5 ....................(ii)

Multiply (ii) with 2,

2x−4y=−10................(iii)

Subtract equations ( ii ) from ( iii ),

⇒(2x+5y)−(2x−4y)=17−(−10)⇒2x+5y−2x+4y=17+10⇒5y+4y=17+10⇒9y=27⇒9y9=279⇒y=3

Substituting y=3 in ( ii ),

⇒x−2y=−5⇒x−2(3)=−5⇒x−6=−5⇒x−6+6=−5+6⇒x=1

Conclusion:

Therefore, the unique solution to the equation is (x,y)=(1,3).

Chapter 5.7, Problem 10MRE

Chapter 5.7, Problem 12MRE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OE Ch. 5.1 - Prob. 2OE Ch. 5.1 - Prob. 3OE Ch. 5.1 - Prob. 4OE Ch. 5.1 - Prob. 5OE Ch. 5.1 - Prob. 6OE Ch. 5.1 - Prob. 7OE Ch. 5.1 - Prob. 8OE Ch. 5.1 - Prob. 9OE Ch. 5.1 - Prob. 10OE

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