Solving Equation With Multiple Variables

Cadin rents a bouncy house for a birthday party.  It costs $30.00 plus $4.00 per hour.  If he spends a total of $78.00, how many hours did he keep the bouncy house?

• $30.00 - $78.00 = $4.00h

• $78.00 + $30.00 = $4.00h

• $30.00 + $4.00h = $78.00

• $30.00 - $4.00h = $78.00

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value? 

• 15x + 2.5 = 10x + 3

• 15 - 2.5x = 10 - 3x

• 15 + 2.5x = 10 + 3x

• 15 - 10 = 2.5x + 3x

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal?

• 150x + 24 = 180 + 20x

• 150 + 24x = 180 + 20x

• 180 - 150 = 24 x + 20x

• 150 - 24x = 180 - 20x

Two or more linear equations with the same variables

• Set of Linear Equations

• System of Linear Equations

• Process of Linear Equations

• Multiple Linear Equations

Solve:
12x - 4y = 20  ,  for   y 

• y = 3x - 5

• y = -3x + 5

• y = -3x - 5

• y = 3x + 5

7(-3x + 10) = 5(-4x + 15)

• x = 7

• x = -5

• x = 5

• x = -7

3k+2(5k-3)=7

• k=1

• k=12

• k=2

• k=5

Solve:
12x - 4y = 20  ,  for   y 

Answer explanation

To solve for y, rearrange the equation: 12x - 4y = 20. First, isolate -4y: -4y = -12x + 20. Then, divide by -4: y = 3x - 5. Thus, the correct answer is y = 3x - 5.

-2x + 35 = 5(-5 - 7x) - 6

• -3

• 11

• 13

• -2

57 = 2 (1 + 5n) - 5 (1 + 6n)

• 3

• -3

• 9

• -9