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Chapter 6: Q25. (page 390)

Use elimination to solve each system of equations.

x+y=13x鈭�y=5

Short Answer

Expert verified

The solution of the system of equations is (9,4).

Step by step solution

01

Step 1. State the concept of elimination method to solve system of equations.

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:

x+y=13 鈥� (1)

x鈭�y=5 鈥� (2)

Note that both the equations havelocalid="1647509637136" 3xin opposite signs, therefore, variablelocalid="1647509633311" xcan be eliminated if both equations are added.

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�x+y=13(+)鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌�x鈭�y=5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�夆��2x=18Dividebothsidesby2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�夆�夆�夆�夆��x=9

03

Step 3. Solve for y.

Substitute 9 for xinto the equation (1) and solve fory.

x+y=13(9)+y鈭�9=13鈭�9y=4

The solution is(9,4).

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Most popular questions from this chapter

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

x+3y=12x=鈭�6y

Graph each system and determine the number of solutions that it has. If it has one solution, name it.

2x+y=鈭�45x+3y=鈭�6

Use elimination to solve each system of equations.

x鈭�4y=23x+4y=38

Tionna has saved dimes and quarters in her piggy bank. Define the variables, and write equations to find the number of dimes and quarters. Then solve using the best method for the situation.

$4.00

25 coins

Solve each equation or formula for the variable specified.

x=3y鈭�9, for y
See all solutions

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