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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

1. Solving Systems of Linear Equations by Graphing

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Exercise 5 Page 203

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

y=4

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

5(2-y)+y=- 6

Distribute 5

5 (2) - 5y+y =- 6

Multiply

10-5y+y=- 6

Add terms

10-4y=- 6

Now, we can continue to solve using the Properties of Equality.

10-4y=- 6

LHS-10=RHS-10

10-4y-10=- 6 -10

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Solve for y

Subtract term

- 4y = - 16

.LHS /(- 4).=.RHS /(- 4).

- 4y/- 4 = - 16/- 4

Cross out common factors

- 4y/- 4 = - 16/- 4

Simplify quotient

y=- 16/- 4

- a/- b=a/b

y= 16/4

Calculate quotient

y= 4

The solution to the equation is y=4. We can check our solution by substituting it into the original equation.

5(2-y)+y=- 6

y= 4

5(2- 4)+ 4 ? = - 6

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Simplify

Subtract term

5(- 2)+4? = - 6

a(- b)=- a * b

- 5* 2 +4 ? = - 6

Multiply

- 10 +4 ? = - 6

Add terms

- 6 = - 6

Since the left-hand side is equal to the right-hand side, our solution is correct.

Subchapter links

Try It p.200-201

Self-Assessment for Concepts & Skills p.201

Self-Assessment for Problem Solving p.202

Review & Refresh p.203

Concepts, Skills, & Problem Solving p.203-204