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Pearson Algebra 1 Common Core, 2011
PA
Pearson Algebra 1 Common Core, 2011 View details
2. Multiplying Powers With the Same Base
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Exercise 61 Page 431

Does either of the equations have an isolated variable in it?

(4,7)

Practice makes perfect

When solving a system of equations using substitution, there are three steps.

  1. Isolate a variable in one of the equations.
  2. Substitute the expression for that variable into the other equation and solve.
  3. Substitute this solution into one of the equations and solve for the value of the other variable.

Observing the given equations, it looks like it will be simplest to isolate y in the second equation.

2x+y=15 - 12x+y=5
AddEqn

(II):LHS+1/2x=RHS+1/2x

2x+y=15 y=5+ 12x

Now that we've isolated y, we can solve the system by substitution.

2x+y=15 y=5+ 12x
Substitute

y= 5+1/2x

2x+ 5+ 12x=15 y=5+ 12x
â–¼
(I):Solve for x
SubEqn

(I): LHS-5=RHS-5

2x+ 12x=10 y=5+ 12x
NumberToFrac

a = 2* a/2

42x+ 12x=15 y=5+ 12x
AddFrac

Add fractions

52x=10 y=5+ 12x
MultEqn

(I):LHS * 2/5=RHS* 2/5

52x* 25=10* 25 y=5+ 12x
CommutativePropMult

(I): Commutative Property of Multiplication

x* 52 * 25=10* 25 y=5+ 12x
MultFracByInverse

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

x* 1=10 * 25 y=5+ 12x
IdPropMult

(I): Identity Property of Multiplication

x=10 * 25 y=5+ 12x
MoveLeftFacToNum

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

x= 205 y=5+ 12x
CalcQuot

(I): Calculate quotient

x=4 y=5+ 12x

Great! Now, to find the value of y, we need to substitute x=4 into the second equation.

x=4 y=5+ 12x
Substitute

(II):x= 4

x=4 y=5+ 12( 4)
MoveRightFacToNumOne

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

x=4 y=5+ 42
CalcQuot

(II): Calculate quotient

x=4 y=5+2
AddTerms

(II):Add terms

x=4 y=7

The solution, or point of intersection, to this system of equations is the point (4,7).

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arrow_right Lesson Check p.429
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arrow_right Practice and Problem-Solving Exercises p.429-431
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arrow_right Standardized Test Prep p.431
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Standardized Test Prep 55 (Page 431)
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Standardized Test Prep 58 (Page 431)
arrow_right Mixed Review p.431
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Mixed Review 67 (Page 431)
Mixed Review 68 (Page 431)