Possible Solutions for Linear Equations

Solve the equation.

3x - 2 = x + 10

Mathematical Equivalence

ON

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

• 1 hour

• 2 hours

• 3 hours

• 4 hours

When solving an equation with a fraction, how do you get rid of said fraction?

• Multiply both sides of the equation by the least common denominator.

• Leave the fraction and move on.

• Multiply both sides of the equation by the numerator.

• Divide both sides of the equation by its reciprocal.

Solve the following equation for g.

Sandy is upgrading her Internet service. Fast Internet charges $60 for installation and $50.45 per month. Quick Internet has free installation but charges $57.95 per month.

The equation that represents this scenario is 60 + 50.45x = 57.95x

• True.

• False.

Simplify and tell whether the equation has one, zero or infinite solutions.

2(3x - 6) = -12 + 6x

• x = 4; One Solution

• x = -x; No Solution

• 0 = 0; Infinite Solutions

• x = 0; One Solution

Fill in the blank with the proper answer choice that will result in the equation having no solution.

8x ​ (a)   = 8x - 6​

• -6

• -8

• 8x

• -8x

Select the answer choice that represents infinite solutions.

• x = x

• x = 4

• x = y

• x= -x

How many solutions does the following system have? Why?
y = -2/3x + 5
2x + 3y = 15

• None.  The equations have the same slope and different  
  y-intercepts

• Infinitely many.  The equations are exactly the same when in slope-intercept form.

• Three.  There are two equations so there are exactly three solutions to the system.

• One.  The equations have different slopes so there is exactly one solution.

What is the solution to the set of equations?
y = -x - 2
y = -5x + 2

•   (3, 1)

•   (1, -3)

•   (-1, -3)

•   (-3, 1)