Question

Consider the following system of equations: 1/3x+y=3,2y=−2/3x+10 Is (0,3) a solution to the system of equations? Explain.

Answer 1

To determine whether the point (0, 3) is a solution to the given system of equations, we need to substitute \(x = 0\) and \(y = 3\) into both equations and check if they hold true.

The first equation is:
\[
\frac{1}{3}x + y = 3
\]
Substituting \(x = 0\) and \(y = 3\):
\[
\frac{1}{3}(0) + 3 = 3
\]
\[
0 + 3 = 3
\]
This is true.

Now, let's check the second equation:
\[
2y = -\frac{2}{3}x + 10
\]
Substituting \(x = 0\) and \(y = 3\):
\[
2(3) = -\frac{2}{3}(0) + 10
\]
\[
6 = 0 + 10
\]
\[
6 = 10
\]
This is false.

Since the second equation is not satisfied by the point (0, 3), we conclude that (0, 3) is **not** a solution to the system of equations.