Determine Systems of Linear Equations

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.

Choose the graph that solves this system of equations.

y = 2x – 6

y = –4x + 3

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The graph solves this system of equations.

–2y = –4x + 8

x + y = 5

• (2,3)

• (3,2)

• (-2,3)

• (-3,2)

The graph solves this system of equations. What is the solution to the system?

• (0,0)

• Infinity many solutions

• No Solution

• Parallel lines

If a system of linear equations has an infinite number of solutions, what do you know about the graph of the system?

• The lines intersect at one point.

• The lines are parallel.

• The lines are the same line.

• The lines cannot be graphed.

The total cost, c, of belonging to two different gyms for m months is shown on the graph. The lines intersect at the point (4, 250). What does the solution means in this situation?

• At 250 months, the cost for each gym is $4

• At 4 months, the cost for each gym is $250

• 250 people get 4 months of membership for free

• 4 people get 250 months of membership for free