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Core Connections Integrated II, 2015

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Core Connections Integrated II, 2015 View details

2. Section 7.2

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Exercise 120 Page 417

Use the Substitution Method.

(- 2, 4)

Practice makes perfect

Since the first equation is already solved for y, we should use the Substitution Method to solve the system of equations.

y=- 3x-2 & (I) 2x+5y=16 & (II)

(II): y= - 3x-2

y=- 3x-2 2x+5( - 3x-2)=16

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(II): Solve for x

(II): Distribute 5

y=- 3x-2 2x-15x-10=16

(II): Subtract term

y=- 3x-2 - 13x-10=16

(II): LHS+10=RHS+10

y=- 3x-2 - 13x=26

(II): .LHS /(- 13).=.RHS /(- 13).

y=- 3x-2 x=- 2

Having solved for x, we can substitute this into the first equation and solve for y.

y=- 3x-2 x=- 2

(I): x= - 2

y=- 3( - 2)-2 x=- 2

MultNegNegOnePar

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

y=6-2 x=- 2

(I): Subtract term

y=4 x=- 2

The system of equations has the solution (- 2, 4). To test our solution, we will substitute this point into the original system and simplify. If the left-hand side and right-hand side are equal, then we have the correct solution.

y=- 3x-2 2x+5y=16

(I), (II): x= - 2, y= 4

4? =- 3( - 2)-2 2( - 2)+5( 4)? =16

(I), (II): Multiply

4? =6-2 - 4+20? =16

(I), (II): Add and subtract terms

4=4 16 = 16

The solution is correct.

Subchapter links

7.2.1 Conditional Probability and Independence p.401-402

7.2.2 More Conditional Probability p.406-409

7.2.3 Applications of Probability p.415-417