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 equations equal (same height)

$1.8x + 3.1 = 2.3x + 1.9$

Step2: Rearrange to isolate x terms

$3.1 - 1.9 = 2.3x - 1.8x$

Step3: Simplify both sides

$1.2 = 0.5x$

Step4: Solve for x

$x = \frac{1.2}{0.5}$

Step5: Round to nearest tenth

$x = 2.4$

Answer:

B. 2.4 weeks