Question
A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
3, x, minus, 10, y, equals, 41
3x−10y=
41
minus, 7, x, minus, 10, y, equals, minus, 29
−7x−10y=
−29
3, x, minus, 10, y, equals, 41
3x−10y=
41
minus, 7, x, minus, 10, y, equals, minus, 29
−7x−10y=
−29
Answers
GPT-4o mini
To eliminate the variable \(y\) from the given system of equations, you should notice that both equations have the same coefficient for \(y\) (which is \(-10\)).
The system of equations provided is:
1. \(3x - 10y = 41\) (Equation 1)
2. \(-7x - 10y = -29\) (Equation 2)
To eliminate \(y\), you can add the two equations together. This will allow the \(-10y\) terms to cancel each other out:
\[
(3x - 10y) + (-7x - 10y) = 41 + (-29)
\]
Performing this addition will give you:
\[
(3x - 7x) + (-10y - 10y) = 41 - 29
\]
Which simplifies to:
\[
-4x - 20y = 12
\]
However, since our goal is just to eliminate \(y\), the correct first step is to simply **add the two equations together**.
So, the first step is:
**Add the two equations to eliminate \(y\).**
The system of equations provided is:
1. \(3x - 10y = 41\) (Equation 1)
2. \(-7x - 10y = -29\) (Equation 2)
To eliminate \(y\), you can add the two equations together. This will allow the \(-10y\) terms to cancel each other out:
\[
(3x - 10y) + (-7x - 10y) = 41 + (-29)
\]
Performing this addition will give you:
\[
(3x - 7x) + (-10y - 10y) = 41 - 29
\]
Which simplifies to:
\[
-4x - 20y = 12
\]
However, since our goal is just to eliminate \(y\), the correct first step is to simply **add the two equations together**.
So, the first step is:
**Add the two equations to eliminate \(y\).**