Answer:
see below
Explanation:
The equation 5x - 7 (x - 1) = ax + b has exactly one solution (True or False)
Distribute the -7 and substitute a and b
5x - 7x+7 = -3x+8
-2x+7 = -3x+8
This has one solution because they are not the same line or parallel lines.
True
The equation 3 (x - 5) - 7 = ax + b has no solution (True or False)
Distribute the 3 and substitute a and b
3x-15 -7 = -3x+8
3x-22 = -3x+8
The slopes are not the same so they are not parallel lines. It has one solution.
False
The equation 2 - 7x + 3 + 4x = ax + b has no solution (True or False)
Substitute in a and b
2 - 7x + 3 + 4x = -3x + 8
Combine like terms
5 -3x = -3x+8
The slopes are the same but the y intercepts are different. The lines will never intersect. They have no solutions
True
The equation -3 (x - 3) - 1 = ax + b has infinitely many solutions (True or False)
Distribute the -3 and substitute a and b
-3 (x - 3) - 1 = -3x + 8
-3x +9 -1 = -3x +8
-3x+8 = -3x+8
This is the same line so it has infinite solutions
True
The equation -5x + 2 + 2x + 4 = ax + b has infinitely many solutions (True or False)
Substitute in a and b
-5x + 2 + 2x + 4 = -3x + 8
-3x+6 = -3x+8
The slopes are the same but the y intercepts are different. These are parallel lines so they do not intersect. There are no solutions
False