1. y = x
y = 2x - 4
Locate the point of intersection of the 2 graphs. This is the solution set of the graphs, that is: (x, y) = (4, 4).
Solution set: (x, y) = (4, 4)
2. y = -
x + 5
y = 3x - 2
Locate the point of intersection of the 2 graphs. This is the solution set of the graphs, that is: (x, y) = (2, 4)
Solution set: (x, y) = (2, 4)
3. y - 2x = 4
y = 2x
Locate the point of intersection of the 2 graphs. The 2 lines are parallel so they do not intersect and therefore no solution set exists for the given set of equations.
Solution set: Does not exist.
4. y - 4x = 8
y = 2(2x +4)
Locate the point of intersection of the 2 graphs. The 2 lines are completely overlapping each other so they intersect intersect at infinite points and therefore infinite solutions exist for the given set of equations.
Solution set: Infinite solutions
5. x + y = 3
y = -3(2x - 1)
Locate the point of intersection of the 2 graphs. This is the solution set of the graphs, that is: (x, y) = (0, 3)
Solution set: (x, y) = (0, 3)
6. -x + y = -2
y = 2
Locate the point of intersection of the 2 graphs. This is the solution set of the graphs, that is: (x, y) = (4, 2)
Solution set: (x, y) = (4, 2)
y = 2x - 4
Locate the point of intersection of the 2 graphs. This is the solution set of the graphs, that is: (x, y) = (4, 4).
Solution set: (x, y) = (4, 4)
2. y = -
y = 3x - 2
Locate the point of intersection of the 2 graphs. This is the solution set of the graphs, that is: (x, y) = (2, 4)
Solution set: (x, y) = (2, 4)
3. y - 2x = 4
y = 2x
Locate the point of intersection of the 2 graphs. The 2 lines are parallel so they do not intersect and therefore no solution set exists for the given set of equations.
Solution set: Does not exist.
4. y - 4x = 8
y = 2(2x +4)
Locate the point of intersection of the 2 graphs. The 2 lines are completely overlapping each other so they intersect intersect at infinite points and therefore infinite solutions exist for the given set of equations.
Solution set: Infinite solutions
5. x + y = 3
y = -3(2x - 1)
Locate the point of intersection of the 2 graphs. This is the solution set of the graphs, that is: (x, y) = (0, 3)
Solution set: (x, y) = (0, 3)
6. -x + y = -2
y = 2
Locate the point of intersection of the 2 graphs. This is the solution set of the graphs, that is: (x, y) = (4, 2)
Solution set: (x, y) = (4, 2)