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

Question

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 $y=2x+1$: $$2=2(1)+1\Rightarrow 2=2+1\Rightarrow 2\ne 3$$ So, (1, 2) does not satisfy this first equation.

2. For $y=5$: $$2\ne 5$$ 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.