body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math: Modeling Real Life, Grade 8

BI

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

Cumulative Practice

Exercise 1 Page 231

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

D

When solving a system of equations using the Substitution Method, there are three steps.

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

For this exercise, y is already isolated in one equation, so we can skip straight to solving!

y=- 2/3x-1 & (I) 4x+6y=- 6 & (II)

(II):y= - 2/3x-1

y=- 2/3x-1 & (I) 4x+6( - 2/3x-1)=- 6 & (II)

(II): Multiply

y=- 2/3x-1 & (I) 4x - 4x-6=- 6 & (II)

(II): Subtract term

y=- 2/3x-1 & (I) - 6=- 6 & (II)

Solving this system of equations resulted in an identity; - 6 is always equal to itself. Therefore, the lines are the same and have infinitely many intersection points, which means there are infinitely many solutions to this system of equations. This corresponds to the answer D.

Subchapter links

Exercises