Question

{-2x + y = 2, 2x + 57 = 19
what is the solution to the system?

(1 1/8 ,4 1/4)
open paren 1 and 1 eighth comma 4 and 1 fourth close paren
(1 2/3 , 5 1/3)
open paren 1 and 2 thirds comma 5 and 1 third close paren
(3 1/4,2 1/2)
open paren 3 and 1 fourth comma 2 and 1 half close paren
(3/4, 3 1/2 )

Answer 1

To solve the system of equations given by:

1. \(-2x + y = 2\)
2. \(2x + 57 = 19\)

We will first solve the second equation:

\[
2x + 57 = 19
\]

Subtract 57 from both sides:

\[
2x = 19 - 57
\]

\[
2x = -38
\]

Now, divide by 2:

\[
x = -19
\]

Now we have \(x = -19\). Next, we substitute this value into the first equation:

\[
-2(-19) + y = 2
\]

Simplifying gives:

\[
38 + y = 2
\]

Subtract 38 from both sides:

\[
y = 2 - 38
\]

\[
y = -36
\]

So the solution to the system is \((-19, -36)\).

Now, let's determine which of the options best matches based on the provided pairs:

1. \( (1 \frac{1}{8}, 4 \frac{1}{4}) \)
2. \( (1 \frac{2}{3}, 5 \frac{1}{3}) \)
3. \( (3 \frac{1}{4}, 2 \frac{1}{2}) \)
4. \( ( \frac{3}{4}, 3 \frac{1}{2}) \)

None of the provided options match the solution \((-19, -36)\). It appears that the pairs provided might have been intended for a different set of equations or there may be an error in the original equations.

Please double-check the equations and options for correctness. If you need help with different numbers or equations, let me know!