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?

Answer 1

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

**Equation 1:**
\[
\frac{1}{3}x + y = 3
\]
Substituting \(x = 0\) and \(y = 3\):
\[
\frac{1}{3}(0) + 3 = 3
\]
This simplifies to:
\[
0 + 3 = 3
\]
This is true.

**Equation 2:**
\[
2y = -\frac{2}{3}x + 10
\]
Substituting \(x = 0\) and \(y = 3\):
\[
2(3) = -\frac{2}{3}(0) + 10
\]
This simplifies to:
\[
6 = 0 + 10
\]
This simplifies to:
\[
6 = 10
\]
This is false.

Since \((0, 3)\) satisfies the first equation but not the second, it is **not a solution** to the system of equations.