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 start by solving the second equation for \(x\).

Step 1: Solve the second equation

Rewrite the second equation: \[ 2x + 57 = 19 \] Subtract 57 from both sides: \[ 2x = 19 - 57 \] \[ 2x = -38 \] Now, divide by 2: \[ x = -19 \]

Step 2: Substitute \(x\) into the first equation

Substitute \(x = -19\) into the first equation: \[ -2(-19) + y = 2 \] This simplifies to: \[ 38 + y = 2 \] Now, isolate \(y\) by subtracting 38 from both sides: \[ y = 2 - 38 \] \[ y = -36 \]

Step 3: Write the solution

The solution to the system of equations is: \[ (x, y) = (-19, -36) \]

Now, let's check the possible answers given:

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 options match the solution we derived, which is \((-19, -36)\).

Therefore, it seems there was some oversight in the choices or in my interpretation from the problem statement itself; none of the provided choices are correct solutions to the system of equations as solved.