Question

Which of the following points is a solution to the system of equations y=23x−5
and y=73x−1
?(1 point)

Answer 1

To find a solution to the system of equations \( y = 23x - 5 \) and \( y = 73x - 1 \), we can set the two equations equal to each other:

\[
23x - 5 = 73x - 1
\]

Now, let's solve for \( x \).

First, we can rearrange the equation to isolate \( x \):

\[
-5 + 1 = 73x - 23x
\]
\[
-4 = 50x
\]

Now, divide by 50:

\[
x = -\frac{4}{50} = -\frac{2}{25}
\]

Next, we can substitute \( x = -\frac{2}{25} \) back into one of the original equations to find \( y \). We'll use the first equation:

\[
y = 23\left(-\frac{2}{25}\right) - 5
\]
\[
y = -\frac{46}{25} - 5
\]
\[
y = -\frac{46}{25} - \frac{125}{25}
\]
\[
y = -\frac{171}{25}
\]

So, the solution to the system of equations is:

\[
\left(-\frac{2}{25}, -\frac{171}{25}\right)
\]

If you have specific points you want to verify as solutions, please provide those points, and I can check if they solve the system.