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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

3. Solving Systems of Linear Equations by Elimination

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Exercise 27 Page 217

Are there any variables already isolated?

Solution: (8/5,-4/5)
Method: See solution.

Practice makes perfect

Since the variable x in the first equation has a coefficient equal to 1, we can isolate it using the Properties of Equality.

x+2y=0 & (I) 2x-y=4 & (II)

(I): LHS-2y=RHS-2y

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

(I): Subtract terms

x=-2y 2x-y=4

Now that x is isolated, the easiest way to solve the system of equations is to use the Substitution Method. Let's substitute x=-2y into the second equation.

x=-2y 2x-y=4

(II): x= -2y

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

▼

(II):Solve for y

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

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

(II): Subtract terms

x=-2y -5y=4

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

x=-2y -5y/-5=4/-5

MovePartNumRight

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

x=-2y -5/-5 * y=4/-5

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

x=-2y 5/5 * y=4/-5

(II): a/a=1

x=-2y 1 * y=4/-5

(II): Identity Property of Multiplication

x=-2y y=4/-5

MoveNegDenomToFrac

(II): Put minus sign in front of fraction

x=-2y y=-4/5

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

x=-2y y=-4/5

(I): y= -4/5

x=-2( -4/5) y=-4/5

▼

(I):Solve for y

MultNegNegOnePar

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

x=2 * 4/5 y=-4/5

MoveLeftFacToNum

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

x=2 * 4/5 y=-4/5

(I): Multiply

x=8/5 y=-4/5

The solution, or point of intersection, of the system of equations is ( 85,- 45).

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