Question

Two rovers are exploring a planet. The system of equations below show each rover's elevation y at time x. Without graphing these equations, what conclusion can you make about the system of equations?Rover A: y = 1.6x - 4Rover B: 3y = 4.8x - 12What conclusion can you make about the system of equations?A. The system has infinity many solutions.B. The system has no solution.C. The system has exactly one solution.

Answer 1

A. The system has infinity many solutions.

we can conclude both rovers have the same road, and they started at the same time

Step-by-step explanation

`\begin{gathered} y=1.6x-4\text{ Equation(1)} \\ 3y=4.8x-12\text{ Equation(2)} \end{gathered}`

Step 1

Let

y represents the elevation

x represents the time

to solve for x, multiply equation(1) by -3 and then add the result to Equation (2)

`\begin{gathered} y=1.6x-4\text{ Equation(1) by -3} \\ -3y=-4.8+4\text{ Equation(3)} \\ \text{now, add equation (3) and equation(2)} \\ \\ -3y=-4.8x+12 \\ 3y=4.8x-12 \\ ----------- \\ 0=0+0 \\ 0=0 \end{gathered}`

when you get a solution like this

`0=0`

it means the system has infinite solutions,so the answer is

A. The system has infinity many solutions.

we can conclude both rovers have the same road, and they started at the same time.

I hope this helps you