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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 25 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 together.

Solution: No solutions.
Explanation: See solution.

Practice makes perfect

Let's consider the given system of equations. 8 x-2 y=16 & (I) - 4 x+ y=8 & (II) Currently, none of the terms in this system will cancel out if we add or subtract the equations. However, if we multiply Equation (II) by 2, both variables will have opposite coefficients. This means that a convenient method to solve this system is the Elimination Method. 8 x-2 y=16 2(- 4 x+ y)=8(2) ⇓ 8 x- 2y=16 - 8 x+ 2y=16 Since the variables have now opposite coefficients, we can add the equations.

8x-2y=16 & (I) - 8x+2y=16 & (II)

(II): Add (I)

8x-2y=16 - 8x+2y+( 8x-2y)=16+ 16

(II): Remove parentheses

8x-2y=16 - 8x+2y+8x-2y=16+16

(II): Add and subtract terms

8x-2y=16 0≠ 32 *

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

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