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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

Chapter Review

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Exercise 28 Page 229

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 or subtracted.

Solution: No solution.
Explanation: See solution.

Practice makes perfect

Consider the given system of equations. 3 x= 13 y+2 & (I) 9 x- y=- 6 & (II) If we multiply the first equation by 3, then the x-variable will have the same coefficient in both equations. Therefore, a convenient method to solve this system is the Elimination Method. Let's solve the system!

3x= 13y+2 9x-y=- 6

(I): LHS * 3=RHS* 3

3x(3)=( 13y+2)3 9x-y=- 6

(I): Distribute 3

3x(3)= 13y(3)+2(3) 9x-y=- 6

(I): Multiply

9x= 13y(3)+6 9x-y=- 6

MoveRightFacToNumOne

(I): 1/b* a = a/b

9x= y3(3)+6 9x-y=- 6

FracMultDenomToNumber

(I): a/3* 3 = a

9x=y+6 9x-y=- 6

(I): LHS-y=RHS-y

9x-y=6 9x-y=- 6

Now, since the variables have the same coefficients in both equations, we can subtract Equation (I) from Equation (II).

9x-y=6 & (I) 9x-y=- 6 & (II)

(II): Subtract (I)

9x-y=6 9x-y-( 9x-y)=- 6- 6

(II): Distribute - 1

9x-y=6 9x-y-9x+y=- 6-6

(II): Add and subtract terms

9x-y=6 0≠ - 12 *

We obtained a false statement. Therefore, the system has no solution.

Subchapter links

1 Solving Systems of Linear Equations by Graphing p.227

2 Solving Systems of Linear Equations by Substitution p.228

3 Solving Systems of Linear Equations by Elimination p.228

4 Solving Special Systems of Linear Equations p.229