Question

Is (2,7) a solution to this system of equations?
y=3x+1
y=2x+5

Answer 1

To determine if the point \((2, 7)\) is a solution to the system of equations given by:

1. \(y = 3x + 1\)
2. \(y = 2x + 5\)

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.