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Big Ideas Math: Modeling Real Life, Grade 8
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Big Ideas Math: Modeling Real Life, Grade 8 View details
3. Solving Systems of Linear Equations by Elimination
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Exercise 26 Page 217

Are there any variables isolated?

Solution: (2,-1)
Method: See solution.

Practice makes perfect
Since the y-variable is already isolated, the easiest way to solve the system of equations is to use the Substitution Method. Let's substitute y=x-3 into the second equation.
y=x-3 & (I) y=-2x+3 & (II)
Substitute

(II):y= x-3

y=x-3 x-3=-2x+3
â–Ľ
Solve for x
AddEqn

(II):LHS+2x=RHS+2x

y=x-3 x-3+2x=-2x+3+2x
AddTerms

(II):Add terms

y=x-3 3x-3=3
AddEqn

(II):LHS+3=RHS+3

y=x-3 3x-3+3=3+3
AddTerms

(II):Add terms

y=x-3 3x=6
DivEqn

(II): .LHS /3.=.RHS /3.

y=x-3 3x/3=6/3
MovePartNumRight

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

y=x-3 3/3 * x=6/3
QuotOne

(II): a/a=1

y=x-3 1 * x=6/3
IdPropMult

(II): Identity Property of Multiplication

y=x-3 x=6/3
CalcQuot

(II): Calculate quotient

y=x-3 x=2
Great! Now, to find the value of y, we need to substitute x=2 into either one of the equations in the given system. Let's use the first equation.
y=x-3 x=2
Substitute

(I):x= 2

y= 2-3 x=2
SubTerms

(I): Subtract terms

y=-1 x=2
The solution, or point of intersection, to this system of equations is the point (2,-1).
Subchapter links expand_more
arrow_right Try It p.212-214
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Try It 2 (Page 212)
Try It 3 (Page 212)
Try It 4 (Page 213)
Try It 5 (Page 213)
Try It 6 (Page 213)
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arrow_right Self-Assessment for Concepts & Skills p.214
Self-Assessment for Concepts & Skills 8 (Page 214)
Self-Assessment for Concepts & Skills 9 (Page 214)
Self-Assessment for Concepts & Skills 10 (Page 214)
Self-Assessment for Concepts & Skills 11 (Page 214)
Self-Assessment for Concepts & Skills 12 (Page 214)
Self-Assessment for Concepts & Skills 13 (Page 214)
Self-Assessment for Concepts & Skills 14 (Page 214)
arrow_right Self-Assessment for Problem Solving p.215
Self-Assessment for Problem Solving 15 (Page 215)
Self-Assessment for Problem Solving 16 (Page 215)
arrow_right Review & Refresh p.216
Review & Refresh 1 (Page 216)
Review & Refresh 2 (Page 216)
Review & Refresh 3 (Page 216)
Review & Refresh 4 (Page 216)
Review & Refresh 5 (Page 216)
arrow_right Concepts, Skills, & Problem Solving p.216-218
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