Question

Which option is a possible solution to a system of linear equations?





Responses

y = 2x + 1
y = 2x + 1

y = 5
y = 5

0
0

(1, 2)
(1, 2)

Answer 1

To determine which option is a possible solution to a system of linear equations, we need to check if any of the given options represent a point that satisfies both equations in the system.

1. **y = 2x + 1**
2. **y = 5**

Let's analyze the options:

- **y = 2x + 1**: This represents one of the equations itself, not a point.
- **y = 5**: This also represents an equation.
- **0**: This is not a point and does not represent a solution to a system.
- **(1, 2)**: This is a point in (x, y) format. Let's check if it satisfies the equations.

We substitute \( x = 1 \) and \( y = 2 \) into both equations:

1. For \( y = 2x + 1 \):
\[
2 = 2(1) + 1 \Rightarrow 2 = 2 + 1 \Rightarrow 2 \neq 3
\]
So, (1, 2) does not satisfy this first equation.

2. For \( y = 5 \):
\[
2 \neq 5
\]
So, it does not satisfy the second equation either.

Since we see that (1, 2) does not satisfy either equation, let's think about the values for x that satisfy both equations, especially the second line:

For \( y = 5\):
Substituting \( y = 5\) into the first equation gives us:
\[
5 = 2x + 1 \Rightarrow 4 = 2x \Rightarrow x = 2
\]
Thus, a point satisfying both equations is \( (2, 5) \).

However, looking only at the options given, none of them provide a valid solution to the system of equations directly. Therefore, the answer is that the point (1, 2) does not satisfy the equations.

To conclude: **None of the provided options are valid solutions to the stated system of linear equations.**