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Big Ideas Math: Modeling Real Life, Grade 8

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Big Ideas Math: Modeling Real Life, Grade 8 View details

3. Solving Systems of Linear Equations by Elimination

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Exercise 13 Page 214

Are there corresponding variables with opposite coefficients?

Solution: (4,1)
Method: See solution.

Practice makes perfect

Notice that the y-variable has opposite coefficients in both equations. If we add the equations, the y-terms will be eliminated. Therefore, we will use the Elimination Method. Let's add Equation (I) to Equation (II), then solve for x.

2x-y=7 & (I) x+y=5 & (II)

(II): Add (I)

2x-y=7 x+y+( 2x-y)=5+( 7)

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(II):Solve for x

(II): Remove parentheses

2x-y=7 x+y+2x-y=5+7

(II): Add and subtract terms

2x-y=7 3x=12

(II): .LHS /3.=.RHS /3.

2x-y=7 3x/3=12/3

MovePartNumRight

(II): a* b/c=a/c* b

2x-y=7 3/3 * x=12/3

(II): a/a=1

2x-y=7 1 * x=12/3

(II): Identity Property of Multiplication

2x-y=7 x=12/3

(II): Calculate quotient

2x-y=7 x=4

Now, we can solve for y by substituting the value of x into either equation and simplifying.

2x-y=7 x=4

(I): x= 4

2( 4)-y=7 x=4

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(I):Solve for y

(I): Multiply

8-y=7 x=4

(I): LHS-8=RHS-8

8-y-8=7-8 x=4

(I): Subtract terms

- y=-1 x=4

(I): LHS * (-1)=RHS* (-1)

-1(- y)=-1(-1) x=4

(I): Multiplication Property of -1

y=1 x=4

The solution, or point of intersection, of the system of equations is (4,1).

Subchapter links

Try It p.212-214

Self-Assessment for Concepts & Skills p.214

Self-Assessment for Problem Solving p.215

Review & Refresh p.216

Concepts, Skills, & Problem Solving p.216-218