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.
- y = 2x + 1
- 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:
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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.
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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.