Question

Consider the following system of equations: 13x+y=32y=−23x+10 Is (0,3) a solution to the system of equations? Explain.

Answer 1

To determine if the point (0,3) is a solution to the given system of equations, we need to verify if it satisfies both equations:

1. The first equation is given as:
\[
13x + y = 32
\]

2. The second equation is given as:
\[
y = -23x + 10
\]

Now, let's substitute \(x = 0\) and \(y = 3\) into both equations and check if they hold true.

**For the first equation:**
\[
13(0) + 3 = 32
\]
This simplifies to:
\[
0 + 3 = 32 \quad \Rightarrow \quad 3 = 32
\]
This is **false**, so the point (0,3) does not satisfy the first equation.

**For the second equation:**
\[
3 = -23(0) + 10
\]
This simplifies to:
\[
3 = 0 + 10 \quad \Rightarrow \quad 3 = 10
\]
This is also **false**, so (0,3) does not satisfy the second equation either.

Since the point (0,3) does not satisfy either of the two equations, we conclude that (0,3) is **not** a solution to the system of equations.