To find the solution to the system of equations given by the lines \( y = 23x - 3 \) and \( y = -13x + 3 \), we need to find the point where the two lines intersect.
We can set the equations equal to each other:
\[ 23x - 3 = -13x + 3 \]
Now, let's solve for \( x \):
- Add \( 13x \) to both sides:
\[ 23x + 13x - 3 = 3 \]
\[ 36x - 3 = 3 \]
- Add 3 to both sides:
\[ 36x = 6 \]
- Divide by 36:
\[ x = \frac{6}{36} = \frac{1}{6} \]
Now that we have \( x = \frac{1}{6} \), we can substitute this value back into one of the original equations to find \( y \). Let's use the first equation:
\[ y = 23\left(\frac{1}{6}\right) - 3 \]
Calculating:
\[ y = \frac{23}{6} - 3 = \frac{23}{6} - \frac{18}{6} = \frac{5}{6} \]
So the solution to the system of equations is:
\[ \left(\frac{1}{6}, \frac{5}{6}\right) \]
Now, let's look at the responses provided:
- There are infinite solutions.
- (6,1)
- There is no solution.
- (0,3)
None of these options match the solution we determined, \(\left(\frac{1}{6}, \frac{5}{6}\right)\). Therefore, it looks like the provided options are incorrect for this system of equations.
1 answer