Bot GPT 4-o mini To determine if the point \((2, 7)\) is a solution to the system of equations given by:
- \(y = 3x + 1\)
- \(y = 2x + 5\)
we need to see if substituting \(x = 2\) into both equations results in \(y = 7\).
For the first equation:
\[ y = 3x + 1 \] Substituting \(x = 2\): \[ y = 3(2) + 1 = 6 + 1 = 7 \]
For the second equation:
\[ y = 2x + 5 \] Substituting \(x = 2\): \[ y = 2(2) + 5 = 4 + 5 = 9 \]
Now we compare the \(y\) values we obtained with the point \((2, 7)\):
- For the first equation, \(y = 7\) (which matches).
- For the second equation, \(y = 9\) (which does not match).
Since \((2, 7)\) satisfies the first equation but not the second equation, it is not a solution to this system of equations.
1 answer