Question

Consider the equation 7x + 4 = ax + b.

for each pair of values for a and b, determine the number of solutions that the equation has.

select no solution, one solution, or infinitely many solutions for each pair of values.

1. a = 7, b = -4

2. a = 4, b = 7

3. a = 7, b = 4

4. a = -7, b = 4

Answer 1

a = 7, b = -4:

This equation can be rewritten as 7x = ax + b - 4.

Since the coefficients of x on both sides are equal, the equation becomes 7x = ax - 4, we can see that the equation has only one solution.

a = 4, b = 7:

This equation can be rewritten as 7x = ax + b - 7.

Since the coefficients of x on both sides are different, the equation becomes 7x = 4x + 7, we can see that the equation has no solution.

a = 7, b = 4:

This equation can be rewritten as 7x = ax + b - 4.

Since the coefficients of x on both sides are equal, the equation becomes 7x = 7x + 4, we can see that the equation has infinitely many solutions.

a = -7, b = 4:

This equation can be rewritten as 7x = ax + b - 4.

Since the coefficients of x on both sides are different, the equation becomes 7x = -7x + 4, we can see that the equation has no solution.

Explanation: