Solving Systems by Graphing

Match a inconsistent system with the number of solutions it has.

• Exactly one

• infinitely many

• no solution

Tags

CCSS.8.EE.C.8B

Match a consistent and dependent system with the number of solutions it has.

• Exactly one

• infinitely many

• no solution

Tags

CCSS.8.EE.C.8B

Match a consistent and independent system with the number of solutions it has.

• Exactly one

• infinitely many

• no solution

Tags

CCSS.8.EE.C.8B

Suppose you graph a system of linear equations. If a point is on only one of the lines, is it a solution of the system? Explain

• Yes; a solution to the system is only on one of the lines.

• No; a solution to the system must be on both lines.

• No; a solution to the systems is not on any of the lines.

• Yes; a solution to the system is either line.

Can a system of two linear equations have exactly two solutions? Explain

• Yes; two lines have two points in common.

• No; two lines do not intersect at any points.

• Yes; two lines can intersect at two points.

• No; two lines intersect at one point, infinite number of points, or not at all.

Without graphing, decide if the system, y = x - 4 and y = x - 3 has one solution, infinitely many solutions, or no solution.

• one solution, equations have the different slopes

• two solution, the lines intersect at two points

• no solution, the slopes are the same and the y-intercepts are different

• infinitely many solutions, the slope and the y-intercept are the same

Tags

CCSS.8.EE.C.8B

Without graphing, decide if the system, 3x + 2y = 4 and 4y = -6x + 8 has one solution, infinitely many solutions, or no solution.

• one solution, equations have the different slopes

• two solution, the lines intersect at two points

• no solution, the slopes are the same and the y-intercepts are different

• infinitely many solutions, the slope and the y-intercept are the same

The first equation in the system is y = 2x - 3. Pick a second equation from the list below so that the system has one solution.

• y = 2x + 4

• y = 1/2x + 2

• -2x + y = -3

• 2y = 4x - 6

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

The first equation in the system is y = 2x - 3. Pick a second equation from the list below so that the system has no solution.

• y = 2x + 4

• y = 1/2x + 2

• -2x + y = -3

• 2y = 4x - 6

Tags

CCSS.8.EE.C.8B

The first equation in the system is y = 2x - 3. Pick a second equation from the list below so that the system has infinitely many solutions.

• y = 2x + 4

• y = 1/2x + 2

• 2x + y = -3

• 2y = 4x - 6

Tags

CCSS.8.EE.C.8B