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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

1. Volumes of Cylinders

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Exercise 7 Page 431

The Elimination Method can be used to solve a system of linear equations if either of the variable terms would cancel out the corresponding variable term in the other equation when added together.

C

Practice makes perfect

To solve a system of linear equations using the Elimination Method, one of the variable terms needs to be eliminated when one equation is added to or subtracted from the other. This means that either the x- or the y-terms must cancel each other out. 3 x+4 y=-10 & (I) 2 x-4 y=0 & (II) We can see that the y-terms will eliminate each other if we add Equation (I) to Equation (II).

3x+4y=-10 2x-4y=0

(II): Add (I)

3x+4y=-10 2x-4y+( 3x+4y)=0+( -10)

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(II):Solve for x

(II): Remove parentheses

3x+4y=-10 2x-4y+3x+4y=0+(-10)

(II): a+(- b)=a-b

3x+4y=-10 2x-4y+3x+4y=0-10

(II): Add and subtract terms

3x+4y=-10 5x=-10

(II): .LHS /5.=.RHS /5.

3x+4y=-10 5x/5=-10/5

MoveNegNumToFrac

(II): Put minus sign in front of fraction

3x+4y=-10 5x/5=-10/5

(II): Factor out 5

3x+4y=-10 5x/5=-5(2)/5

CancelCommonFac

(II): Cancel out common factors

3x+4y=-10 5x/5=-5(2)/5

(II): Simplify quotient

3x+4y=-10 x=-2

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

3x+4y=-10 x=-2

(I): x= -2

3( -2)+4y=-10 x=-2

▼

(I):Solve for y

(I): a(- b)=- a * b

-3 * 2+4y=-10 x=-2

(I): Multiply

-6+4y=-10 x=-2

(I): LHS+6=RHS+6

-6+4y+6=-10+6 x=-2

(I): Add terms

4y=-4 x=-2

(I): .LHS /4.=.RHS /4.

4y/4=-4/4 x=-2

MoveNegNumToFrac

(I): Put minus sign in front of fraction

4y/4=-4/4 x=-2

(I): Factor out 4

4y/4=-4(1)/4 x=-2

CancelCommonFac

(I): Cancel out common factors

4y/4=-4(1)/4 x=-2

(I): Simplify quotient

y=-1 x=-2

The solution, or point of intersection, of the system of equations is (-2,-1). Therefore, the correct option is C.

Subchapter links

Try It p.428-429

Self-Assessment for Concepts & Skills p.429

Self-Assessment for Problem Solving p.430

Review & Refresh p.431

Concepts, Skills, & Problem Solving p.431-432