Solutions for Systems of Linear Equations by Inspection

You can tell this system of equations has one solution because...

• The y-intercepts are the same

• The slopes are the same

• The y-intercepts are different

• The slopes are different

Which system of equations has infinitely many solutions?

• 3y = –5x + 7

  3x = –5y – 7

• 3y = x – 4

  3x – 9y = –12

• 2x + y = 2

  –4x – 2y = 4

• 2y = 3x + 6

  4y = 6x + 12

Which system of equations has no solution?

• 3y = 1 + x

  y = –2x + 5

• 4x – 5y = 3

  –3 = 4x – 5y

• 5x + 4y = 1

  4x – 2y = 4

• y = –3x + 4

  y = (–3/4)x + 1

Each equation in a system of linear equations has the same slope. What are the possible solutions the system could have?

• The system could have no solution or infinitely many solutions.

• The system could have one solution or no solution.

• The system could have one solution.

• The system could have one solution or infinitely many solutions.

Suri makes $15 per hour and gets a weekly bonus of $25. Juan makes $14 per hour and gets a weekly bonus of $50. Is it possible for Suri and Juan to make the same amount of wages, y, by working the same number of hours, x, in one week?

• Yes because the slopes of the equations are different so the system of equations will have one solution.

• No because the slopes of the equations are the same so the system of equations will have no solution.

• Yes because the slopes of the equations are the same so the system of equations will have no solution.

• No because the slopes of the equations are different so the system of equations will have one solution.

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

3x - 8 = 3(x - 4) + 1

• one

• no solutions

• infinite solutions

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

3x - 7 = 3(x - 3) + 2

• one

• no solutions

• infinite solutions

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.
5x + 6 = 2 + 3x

• one
• no solutions
• infinite solutions

Solve:
2x + 1 = 2x - 1

• No Solution
• x = 0
• Infinitely Many Solutions

Solve:
3x + 15 = 3(x + 5)

• No Solution
• x = 15
• Infinitely Many Solutions