Question

Solve.

y=2x−6


4x−2y=14


Use the substitution method.

Responses

There is no solution.
There is no solution.

The solution is (4,14).
The solution is (4,14).

There are an infinite number of solutions.
There are an infinite number of solutions.

The solution is (14,4).
The solution is (14,4).

Answer 1

Substitute y = 2x − 6 into 4x − 2y = 14:

4x − 2(2x − 6) = 14
4x − 4x + 12 = 14
12 = 14 (false)

This contradiction means the system is inconsistent — the lines are parallel (y = 2x − 6 and y = 2x − 7), so there is no solution.