Question

use the following scenario: cell phone company a charges $55 per month plus a flat rate of $50 for all text messages sent for the length of the contract. cell phone company b charges $55 per month plus a flat rate of $95 for all text messages sent for the length of the contract. let x = months charged, let y = total cost, and let the system of equations represent the situation above: ( y = 55x + 50 ) ( y = 55x + 95 ) examine the graph of the situation above. what is the solution? choose one correct answer. graph shown options: - where the lines intersect will be the solution. - there are infinitely many solutions because both equations represent the same line. - there is no solution because the lines are parallel. - (0,5) is the solution.

Explanation:

To solve this, we analyze the system of equations \( y = 55x + 50 \) and \( y = 55x + 95 \).

Step 1: Analyze the slopes

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope. For both equations, the slope \( m = 55 \).

Step 2: Analyze the y-intercepts

The y-intercept \( b \) is different: \( 50 \) for the first line and \( 95 \) for the second line.

Step 3: Determine the relationship between the lines

Lines with the same slope but different y-intercepts are parallel. Parallel lines never intersect, so there is no solution (no point \((x, y)\) that satisfies both equations).

Answer:

There is no solution because the lines are parallel.