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Chapter 6: Q30. (page 338)

Use elimination to solve each system of equations.

x鈭�4y=23x+4y=38

Short Answer

Expert verified

The solution of the system of equations is(10,2).

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鈭�4y=2 鈥� (1)

3x+4y=38 鈥� (2)

Note that both the equations have 4yin opposite signs, therefore, variable ycan 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鈭�4y=2(+)鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌�3x+4y=38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��4x=40Dividebothsidesby4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=10

03

Step 3. Solve for y.

Substitute 10 for xinto the equation (1) and solve for y.

x鈭�4y=210鈭�4y鈭�10=2鈭�10鈭�4y=鈭�8y=2

The solution is (10,2).

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