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.
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.