Question

Answer two questions about Systems AAA and BBB:

System AAA \text{\quad}start text, end text System BBB
\begin{cases}-3x+12y=15\\\\7x-10y=-2\end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
​

−3x+12y=15
7x−10y=−2
​
\begin{cases}-x+4y=5\\\\7x-10y=-2\end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
​

−x+4y=5
7x−10y=−2
​

1) How can we get System BBB from System AAA?

Answer 1

1. To get System BBB from System AAA, we can divide both sides of the first equation in System AAA by -3:

-3x + 12y = 15

-3x/ -3 + 12y/ -3 = 15/ -3

x + 4y = -5

So System BBB is obtained by dividing both sides of the first equation in System AAA by -3.

2. Are Systems AAA and BBB equivalent?

Yes, Systems AAA and BBB are equivalent. This means that they have the same solution set, despite having different coefficients in their equations. Equivalent systems of linear equations are systems that have the same solution set, regardless of the coefficients of the equations.