Consider the system of equations below.

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:

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

Let's first solve the second equation for \(x\):

\[ 2x + 57 = 19 \] Subtracting 57 from both sides:

\[ 2x = 19 - 57 \] \[ 2x = -38 \] Dividing both sides by 2:

\[ x = -19 \]

Now we substitute \(x = -19\) into the first equation to find \(y\):

\[ -2(-19) + y = 2 \] \[ 38 + y = 2 \] Subtracting 38 from both sides:

\[ y = 2 - 38 \] \[ y = -36 \]

The solution to the system is:

\[ (x, y) = (-19, -36) \]

Now we check against the options provided:

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

None of these options match the values we found, indicating there might have been a misunderstanding in forming the equations, the calculations, or the provided answer options.

However, based on our calculations:

The solution to the equations is \( (-19, -36) \), which does not match any of the answer choices provided. Please verify the equations or the options.