Question

100y + 50x = 100

-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:

\((0, 1)\)