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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

4. Solving Special Systems of Linear Equations

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Exercise 1 Page 220

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.

No solution.

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. y=- x+3 & (I) y=- x+5 & (II) We can see that both x- and y-terms will eliminate each other if we subtract Equation (I) from Equation (II). Let's do it!

y = - x + 3 y = - x + 5

(II): Subtract I

y = - x + 3 y - y= - x + 5 - ( - x + 3)

Distribute - 1

y = - x + 3 y - y= - x + 5 +x-3

Subtract terms

y = - x + 3 0= 2

We can see that the second is always false. y = - x + 3 0= 2 * This means that the system has no solution.

Subchapter links

Try It p.220-221

Self-Assessment for Concepts & Skills p.221

Self-Assessment for Problem Solving p.222

Review & Refresh p.223

Concepts, Skills, & Problem Solving p.223-224