Question

Consider the following system of equations:

{
3
1
​
x+y=3
2y=−
3
2
​
x+10
​

0
/
2
11.
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 system of equations, we will substitute \( x = 0 \) and \( y = 3 \) into both equations and see if they hold true.

The system of equations is:

1. \( x + y = 3 \)
2. \( 2y = -\frac{3}{2}x + 10 \)

Now, let's substitute \( (0, 3) \) into these equations.

### First Equation:
Substituting into \( x + y = 3 \):
\[
0 + 3 = 3
\]
This simplifies to:
\[
3 = 3
\]
This equation holds true.

### Second Equation:
Substituting into \( 2y = -\frac{3}{2}x + 10 \):
\[
2(3) = -\frac{3}{2}(0) + 10
\]
This simplifies to:
\[
6 = 0 + 10
\]
So, we have:
\[
6 = 10
\]
This equation does not hold true.

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.