Question

interpreting a solution to a system of linear equations
students graphed the growth rate over several weeks of two plants in their classroom. the equations of both plants are given where x represents the time in weeks and y represents the heights of the plants in inches.
plant a: ( y = 1.8x + 3.1 )
plant b: ( y = 2.3x + 1.9 )
approximately how many weeks will it take for both plants to reach the same height? round your answer to the nearest tenth.
○ 1.9 weeks
○ 2.4 weeks
○ 3.1 weeks
○ 7.4 weeks

Explanation:

Step1: Set the equations equal

Since the heights \( y \) are equal when the plants are the same height, set \( 1.8x + 3.1 = 2.3x + 1.9 \).

Step2: Solve for \( x \)

Subtract \( 1.8x \) from both sides: \( 3.1 = 0.5x + 1.9 \).
Subtract \( 1.9 \) from both sides: \( 1.2 = 0.5x \).
Divide both sides by \( 0.5 \): \( x = \frac{1.2}{0.5} = 2.4 \).

Answer:

2.4 weeks