Solving Systems by Graphing

Front

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

Back

no solution

Front

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

Back

infinitely many

Front

Match a consistent and independent system with the number of solutions it has. Options: Exactly one, infinitely many, no solution

Back

Exactly one

Front

If a point is on only one of the lines in a system of linear equations, is it a solution of the system?

Back

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

Front

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

Back

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

Front

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

Back

No solution, the slopes are the same and the y-intercepts are different.

Front

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

Back

Infinitely many solutions

Front

First equation: y = 2x - 3. Pick a second equation for one solution: y = 2x + 4, y = 1/2x + 2, -2x + y = -3, 2y = 4x - 6.

Back

y = 1/2x + 2

Front

First equation: y = 2x - 3. Pick a second equation so that the system has no solution: y = 2x + 4, y = 1/2x + 2, -2x + y = -3, 2y = 4x - 6.

Back

y = 2x + 4

Front

First equation: y = 2x - 3. Pick a second equation for infinitely many solutions: y = 2x + 4, y = 1/2x + 2, 2x + y = -3, 2y = 4x - 6.

Back

2y = 4x - 6