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Chapter 3: Q22. (page 143)

Solve each system of equations

r+s+t=52r鈭�7s鈭�3t=1312r鈭�13s+23t=鈭�1

Short Answer

Expert verified

The solution set of the given system of equations is .(8,3,鈭�6)

Step by step solution

01

– Use the elimination method to get the system of equations in two variables.

Multiply the equation r+s+t=5by 3and add the new resultant equation to the equation 2r-7s-3t=13.

鈥夆赌�r+鈥夆赌夆��s+鈥夆赌�t=鈥夆赌夆��52r鈭�7s鈭�3t=13_鈥夆赌夆�夆赌�multiplyby3鈫�鈥夆赌�3r+3s+3t=152r鈭�7s鈭�3t=13_鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌�5r鈭�4s+鈥�0=鈥�28

So, the resultant equation is 5r-4s=28.

Next, multiply the equation r+s+t=5by 4and multiply the equation 12r-13s+23t=-1by 6.

Then subtract the two new resultant equations

鈥夆赌夆��r+鈥夆赌夆��s+鈥夆赌夆�夆赌�t=鈥夆赌�512r鈭�13s+23t=鈭�1_鈥夆赌夆�夆赌�multiplyby4鈫�multiplyby6鈫�鈥夆赌�鈥夆赌夆�夆赌夆��4r+4s+4t=20(鈭�)3r鈭�2s+4t=鈭�6_鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌�r+6s+鈥夆赌夆��0=26

So, the resultant equation is r+6s=26

02

– Use the elimination method to solve the system of two equations.

Multiply 5r-4s=28by 3 and multiply the equation r+6s=26by 2.

Then add the two new resultant equations.

5r鈭�4s=28鈥夆赌�r+6s=26_鈥夆赌夆�夆赌�multiplyby3multiplyby2鈥夆赌�15r鈭�12s=84鈥夆赌�2r+12s=鈥�52_鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌�17r+鈥夆赌夆�夆赌夆��0=136

Solve 17r=136for r:

17r=13617r17=13617鈥夆赌夆�夆赌夆�夆赌塂ividebothsidesby17r=8

03

– Find the values of sand t.

Substitute$r=8$in\[r+6s=26\]and find the value of s.

r+6s=268+6s=26鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌塖ubstitute8forr6s=18鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌塖ubtract8frombothsidess=3鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌塂ividebothsidesby6

Substitute r=8,s=3inr+s+t=5and find the value of t.

r+s+t=58+3+t=5鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌塻ubstitute8forr,3fors11+t=5鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌塻implifyt=鈭�6鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌塖ubtract11鈥塮谤辞尘产辞迟丑蝉颈诲别蝉

Hence, the solution of the given system of equations isr,s,t=8,3,-6.

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Most popular questions from this chapter

For Exercises 39-41, use the following information.

Adam and his family are planning to rent a midsize car for one-day trip. In the Standard Rental Plan, they can rent a car for \(52 per day plus 23 cents per mile. In the Deluxe Rental Plan, they can rent a car for \)80 per day with unlimited mileage.

39. For each plan, write an equation that represents the cost of renting a car.

Solve each system of equations by graphing.

3x鈭�7y=鈭�6x+2y=11

Stamps Paula bought $22.82 worth of 49-cent

stamps and 21-cent stamps. The number of 21-cent

stamps was eight less than the number of

49-cent stamps. Solve the equation

0.49s + 0.21(s 鈭� 8) = 22.82 for s, to find the number

of 49-cent stamps Paula bought.

Solve each system of inequalities by graphing.

y鈮�x-3y鈮�-x+1

1.2x-0.91=0.8x+2.29
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