ToSolve:The system of linear equations

3x−2y=−5

4x+5y=47

Expert Solution & Answer

Answer to Problem 16E

The solution of the given system of linear equations is (x,y)=(3,7)

Explanation of Solution

Given:

The system of linear equations

3x−2y=−5

4x+5y=47

Concept Used:

In solving a system of linear equation by substitution method. The value of one of the unknown from any of the equation is substituted into another equation and the value of second unknown is calculated.

The calculated value of second unknown is then substituted into any of the equation to find the value of the first unknown.

Calculation:

Given the system of linear equations

3x−2y=−5 - - - - - (1)

4x+5y=47 - - - - - (2)

Using the Substitution method

From equation (1)

3x−2y=−53x−2y+2y=−5+2y Add 2y to both sides3x=−5+2y3x3=−53+2y3 Divide both sides by 3

x=−53+2y3

Substituting the value of x from equation (1) into the equation (2) , we have

4x+5y=474(−53+2y3)+5y=47 Substitue −53+2y3 for x−203+8y3+5y=47−203+8y3+5y+203=47+203 Add 203 to both sides

8y3+5y=47+2038y3+15y3=1413+20323y3=1613(23y3)(323)=(1613)(323) Multiply by 323 to both sides

y=7

Substituting y=7 into equation (1)

3x−2y=−53x−2(7)=−5 Substitue y=73x−14=−53x−14+14=−5+14 Add 14 to both sides

3x=93x3=93 Divide both sides by 3x=3

Therefore, the solution of the given system of linear equations is (x,y)=(3,7)

Conclusion:

The solution of the given system of linear equations is (x,y)=(3,7)

Chapter 5.4, Problem 15E

Chapter 5.4, Problem 17E

Chapter 5 Solutions

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

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

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Prob. 6E Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Prob. 21E Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - 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