Question
Fill in the blanks so that the following system of linear equations has infinite solutions.
y
=
2
x
+
7
y=2x+7
y
=
y=
x
+
x+
Answers
GPT-4o mini
To ensure that the system of linear equations has infinite solutions, the two equations must be equivalent. This means that the second equation must be a rearranged version of the first.
The first equation is:
\[
y = 2x + 7
\]
To write the second equation in a form that is equivalent to the first equation, we can simply express \(y\) again as \(2x + 7\).
So, we have:
\[
y =
2x +
7
\]
Thus, the complete form of the second equation is:
\[
y = 2x + 7
\]
Alternatively, depending on the specific format you are looking for, you can express it as:
\[
y = 2x + m
\]
where \(m=7\) to keep it equivalent to the first line.
In this way, both equations represent the same line, creating infinite solutions.
The first equation is:
\[
y = 2x + 7
\]
To write the second equation in a form that is equivalent to the first equation, we can simply express \(y\) again as \(2x + 7\).
So, we have:
\[
y =
2x +
7
\]
Thus, the complete form of the second equation is:
\[
y = 2x + 7
\]
Alternatively, depending on the specific format you are looking for, you can express it as:
\[
y = 2x + m
\]
where \(m=7\) to keep it equivalent to the first line.
In this way, both equations represent the same line, creating infinite solutions.