Unit 4 Review

Unit 4 Review
Linear Equations and Linear Systems

TOPIC 1

Solving Any Linear Equation

To solve an equation, make balanced moves to get the equation in the form .

Generally, use these steps to solve:

• distribute to eliminate parentheses;

• collect like terms on each side;

• add or subtract to get the variable on one side and the constant on the other; and

• multiply or divide to get the variable.

Number of Solutions

If an equation can be simplified so that the left and the right sides:

• have different variable terms, then the equation has one solution;

• simplify to the same expression, then the equation is true for all values of and has an infinite number of solutions; and

• simplify to have the same variable expression, but different constants, then the equation is not true for all values of and has no solution.

Match

Match the following

• solution

• systems of equations

• term

a value that makes an equation true

a set of two or more equations

a part of an expression

• a value that makes an equation true

• a set of two or more equations

• a part of an expression

Multiple Choice

• 1

• 2

• 3

• 4

TOPIC 2: solving systems of equations

Multiple Choice

A theater group sold refreshments during intermission as a fundraiser. They sold bottles of water for $2 and fruit cups for $4. They sold 100 items and made $250.

Which system of equations best represents this scenario if x represents the number of bottles of water sold and y represents the number of fruit cups sold?

• x+y=250

  2x+4y=100

• x+y=250

  x+y=100

• x+4y=250

  x+4y=100

• 2x+4y=250

  x+y=100

Match

Match the following

• one solution

• no solution

• infinitely many solutions

y=2x+5

y=-3x-4

y=5x+9

y=5x+2

y=x+4

y=x+4

• y=2x+5

  y=-3x-4

• y=5x+9

  y=5x+2

• y=x+4

  y=x+4

Multiple Choice

What is the solution to the system of equations graphed to the left?

• (0,0)

• (2,3)

• (3,2)

Multiple Choice

Set up the following system of equations to solve.

y=2x+5

y=3x-1

• y=2(3x-1)+5

• 2x+5=3x-1

• 3(2x+5)-1=y

Multiple Choice

Maila and her younger cousin measure their heights. They notice that Maila is 8 inches taller, and their heights add up to exactly 100 inches. Let x represent the cousins height and y represent Maila's height. Which system of equations represents this situation.

• x+y=8

  y=x+100

• x+y=100

  y=x+8

• x+y=100

  x+y=8

Multiple Choice

What is the solution to this system of equations

x+y=100

y=x+8

• (46,54)

• (54,46)

• (50,50)