Question

Consider the system of equations below.
-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, we first rewrite the equations clearly:

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

Let's solve Equation 2 for \(x\):

\[
2x + 57 = 19
\]

Subtract 57 from both sides:

\[
2x = 19 - 57
\]

\[
2x = -38
\]

Now, divide both sides by 2:

\[
x = -19
\]

Now that we have \(x = -19\), we substitute this value into Equation 1 to find \(y\):

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

This simplifies to:

\[
38 + y = 2
\]

Now, subtract 38 from both sides:

\[
y = 2 - 38
\]

\[
y = -36
\]

Thus, the solution to the system of equations is \((-19, -36)\).

Now, let's compare this solution with the provided answer options:

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

Since none of the provided answer options match \((-19, -36)\), it seems that none of the options are the correct solution for the system of equations given.