Question

Examine the different equations that follow:

1. y = 5x - 4

2. y = - 2x + 3

3. y = 3x + 1

4. 2y = 6x + 2

5. y - 5x = 2

6. y - 4x + 1 = 0

7. v = 5x

Complete steps a. through e. to determine which pair of equations form a system with one solution, no solution, or infinite solutions.

a. Solve each equation and make sure it is in y = mx + b format.

Answer 1

1. y = 5x - 4
2. y = -2x + 3
3. y = 3x + 1
4. y = 3x + 1 (after dividing by 2)
5. y = 5x + 2 (after rearranging)
6. y = 4x - 1 (after rearranging)
7. v = 5x

b. Graph each pair of equations on the same coordinate plane.

c. Determine if the lines are parallel, intersecting at one point, or overlapping.

1. and 2. form a system that intersect at one point, as the lines have different slopes and intercepts.

3. and 4. form a system with infinite solutions, as they represent the same line when simplified.

5. and 6. form a system with no solution, as the lines are parallel and have different slopes.

7. and 1. form a system with one solution, as they have different slopes and intercepts.