one winter day, the outside temperature, y, never dropped below -1°. the inside temperature, x, of a car was…

one winter day, the outside temperature, y, never dropped below -1°. the inside temperature, x, of a car was always at least 4° warmer than the outside temperature. which graph represents the solution to the system of inequalities that models this situation?

one winter day, the outside temperature, y, never dropped below -1°. the inside temperature, x, of a car was always at least 4° warmer than the outside temperature. which graph represents the solution to the system of inequalities that models this situation?

Answer

Answer:

The correct graph represents the system ( y \geq -1 ) and ( x \geq y + 4 ).

Explanation:

Step 1: Translate the first condition to an inequality

The outside temperature ( y ) never dropped below (-1^\circ), so ( y \geq -1 ). This is a horizontal solid line at ( y = -1 ) with shading above.

Step 2: Translate the second condition to an inequality

The inside temperature ( x ) was always at least ( 4^\circ ) warmer than ( y ), so ( x \geq y + 4 ). Rearranged as ( y \leq x - 4 ), this is a solid line with slope 1 and y-intercept (-4), shading below.

Step 3: Identify the solution region

The solution is the intersection of ( y \geq -1 ) and ( y \leq x - 4 ), which is the area above ( y = -1 ) and below ( y = x - 4 ).