Question

Write and solve a system of equations made up of Aiden's and Natalie's lines of best fit that they can useto find the catapult arm length that they could both use to launch their tennis balls the same distance.What is the solution to the system?Type the correct answer in the box. Round each number to the nearest tenth.Aiden:y=2.3x+160.7Natalie:y=3.6x+202.6

Answer 1

Given

Aiden:y=2.3x+160.7

Natalie:y=3.6x+202.6

`\begin{gathered} y=2.3x+160.7\ldots\text{Equation i} \\ y=3.6x+202.6\ldots\text{Equation i}i \\ \end{gathered}`

We can use the substitution method

Step 1

Substitute for y=2.3x+160.7 in equation ii

`\begin{gathered} 2.3x+160.7=3.6x+202.6 \\ \text{collect the like terms} \\ 2.3x-3.6x=202.6-160.7 \\ -1.3x=41.9 \\ \text{divide both sides by }-1.3 \\ -(1.3x)/(-1.3)=-(41.9)/(1.3) \\ \\ x=-32.23076923 \end{gathered}`

Step 2

Now to find y we can substitute to either equation i or ii

`\begin{gathered} Using\text{ equation i} \\ y=2.3x+160.7 \\ y=2.3(-32.23076923)+160.7 \\ y=-74.13076923+160.7 \\ y=86.56923077 \end{gathered}`

The final answer to nearest tenth

x = -32.2

y= 86.6