Comparing Slopes in Systems of Linear Equations

Which of the equations has only one solution? 

(you have to change from the standard form to slope intercept)

• A

  x + 3y =3  y =- 1/3 x +1

• B

  3x + y = 3 y = 3x + 1

• C

  x + y = 3

  y = -3x + 1

• x + 3y = 3

  y= -1/3x -1

Answer explanation

The equations of the system have different slopes and y-intercepts. So the system has exactly one solution

Which system of the equation has no solutions? (a)  

• A One solution
• B Infinitively many solutions
• C No solution
• D Positively solutions

Answer explanation

The lines have the same slope but different y-intercepts. No point in the graph satisfies both equations. So the system has no solution.

Which system of the equation has infinitely many solutions?

• A

  2x -5y =5

  y = -2/3x +1

• B

  5x +2y = 5

  y = -5/2x +1

• C

  2x +5y =5

  y = -2/5x +1

• D

  5x + 2y = 5

  y = 5/2 x +1

Answer explanation

Both equations have the same slope and y-intercepts, so the graph is in the same line. Since all points on the graph satisfy the system, the system has an infinitely many numbers of solutions.

which equation form with y = 5x +3

a system of equations that has only one solution

• A

  -5x + y =3

• B

  5x -y = -3

• C

  5x -y = 3

• D

  5x + y = 3

Answer explanation

The system of equations has only one solution.

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (0, 1)

How many solutions does this system of equations have?

• One Solution
• No solution
• Infinitely Many Solutions
• Two Solutions

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines
• the same line 
• Intersecting lines

Parallel Lines never intersect because...

• they have the same slopes. 
• they have the same y-intercept.
• they have different slopes.
• they have different y-intercepts. 

Solve the system of equations.

• (11, 21)

• (3, 11)

• (11, -67)

• No solution

• Infinite solutions