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Chapter 6: Q37. (page 330)

Use elimination to solve each system of equations.

鈭�9x+3y=鈭�33x鈭�2y=鈭�4

Short Answer

Expert verified

The solution of the system of equations is (2,5).

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:

鈭�9x+3y=鈭�3 鈥� (1)

3x鈭�2y=鈭�4 鈥� (2)

Multiply equation (2) by 3.

role="math" localid="1647515977163" 3脳(3x鈭�2y)=3脳(鈭�4)9x鈭�6y=鈭�12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�(3)

Note that both the equations (1) and (3) have 9xin opposite signs, therefore, variable 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�鈭�9x+3y=鈭�3(+)鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�9x鈭�6y=鈭�12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��鈭�3y=鈭�15Dividebothsidesby鈭�3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��y=5

03

Step 3. Solve for x.

Substitute 5 foryinto the equation (2) and solve forx.

3x鈭�2y=鈭�43x鈭�2(5)+10=鈭�4+103x=6x=2

The solution is(2,5).

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Most popular questions from this chapter

Use elimination method to solve the system of equations below:

3x+2y=鈭�22x鈭�2y=鈭�18

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x鈭�y=8y=鈭�3x

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x+y鈮�5y鈮�x+2

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