100y + 50x = 100

Question

-25x +50y =50

Group of answer choices

(0,1)

(-100, 100)

(1, 100)

(100, 1)

Answer 1

To solve the system of equations given by

1. \( 100y + 50x = 100 \)
2. \( -25x + 50y = 50 \)

we can rewrite these equations in a more manageable form and check the provided answer choices.

First, let's simplify both equations.

1. Divide the first equation by 50:

   \[ 2y + x = 2 \quad \text{(Equation 1)} \]

2. Divide the second equation by 25:

   \[ -x + 2y = 2 \quad \text{(Equation 2)} \]

Now we can rearrange Equation 1 to express \(x\) in terms of \(y\):

\[ x = 2 - 2y \]

Next, substitute \(x\) into Equation 2:

\[ -(2 - 2y) + 2y = 2 \]

Distributing the negative:

\[ -2 + 2y + 2y = 2 \] \[ 4y - 2 = 2 \] \[ 4y = 4 \] \[ y = 1 \]

Now substitute \(y = 1\) back into the equation for \(x\):

\[ x = 2 - 2(1) = 0 \]

So we have the solution:

\[ (x, y) = (0, 1) \]

None of the other answer choices (-100, 100), (1, 100), (100, 1) are valid solutions.

Thus, the correct answer is:

\((0, 1)\)