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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 4 Page 203

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

c=8

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, the variable term is already on the left-hand side of the equation, so we will start by subtracting 3 from both sides.

3/4c-1/4c+3=7

LHS-3=RHS-3

3/4c-1/4c+3-3=7-3

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Solve for c

Subtract term

3/4c-1/4c=4

Subtract fractions

2/4c=4

a/b=.a /2./.b /2.

1/2c=4

MoveRightFacToNum

a/c* b = a* b/c

c/2=4

LHS * 2=RHS* 2

c/2* 2=4 * 2

FracMultDenomToNumber

a/2* 2 = a

c=4 * 2

Multiply

c=8

The solution to the equation is c=8. We can check our solution by substituting it into the original equation.

3/4c-1/4c+3=7

c= 8

3/4* 8-1/4* 8+3? =7

▼

Simplify

MoveRightFacToNum

a/c* b = a* b/c

3* 8/4-1 * 8/4+3? = 7

Multiply

24/4-8/4+3? = 7

Subtract fractions

16/4+3? = 7

Calculate quotient

4+3? = 7

Add terms

7=7

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