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 heights equal (same height)

$1.8x + 3.1 = 2.3x + 1.9$

Step2: 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: Calculate and round

$x = 2.4$

Answer:

2.4 weeks