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Chapter 6: Q49. (page 391)

Determine the best method to solve each system of equations. Then solve the system.

3x+4y=262x+3y=19

Short Answer

Expert verified

The best method to solve the system of equations is Elimination method.The solution of the system of equations is (2,5).

Step by step solution

01

Step 1. State the concept of substitution method and elimination method.

The substitution method is used to find the set of solutions for the given system of equations. It is the method in which one variable is first solved in the form of another variable.

So, the value of one variable in the form second variable is put on the second equation. It will give the solution of the one variable. And then solve it for another variable.

The elimination method is the method in which addition or subtraction method is used to get an equation in the one variable.

If the coefficients are opposite, use the addition and when the coefficients are same, use the subtraction.

02

Step 2. Add or subtract the equations to eliminate one variable.

The given system of equation is:

3x+4y=26 鈥� (1)

2x+3y=19 鈥� (2)

Multiply equation (1) by 2.

2(3x+4y)=2脳(26)6x+8y=52鈥�.....鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�(3)

Multiply equation (2) by 3.

3(2x+3y)=3脳(19)6x+9y=57鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�.....(4)

Note that both the equations (3) and (4) have 6xin same signs, therefore, variable xcan be eliminated if both equations are subtracted.

鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�6x+8y=52(鈭�)鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�6x+9y=57炉鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆�夆�夆�夆�夆�夆�夆�夆�夆�夆��鈭�y=鈭�5鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�y=5

03

Step 3. Solve for x.

Substitute 5 for y into the equation (1) and solve for x.

3x+4y=263x+4(5)鈭�20=26鈭�203x=6x=2

The solution is (2,5).

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Most popular questions from this chapter

A home goods store received \(881from the sale of 4 table saws and 9 electric drills. If the receipts from the saws exceeded the receipts from the drills by \)71, what is the price of an electric drill?

F\(45 G\)59 H\(108 J \)119

The perimeter of a rectangle is 48 inches. The length is 6 inches greater than the width. Define the variables, and write equations to represent this situation. Solve the system by using substitution.

Use substitution to solve each system of equations.

y=5x鈭�3x+2y=27

Determine the best method to solve each system of equations. Then solve the system.

y=鈭�xy=2x

Use elimination to solve each system of equations.

x鈭�4y=23x+4y=38
See all solutions

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