Consider the system of equations.

To find the solution of the system of equations, we can set the two equations equal to each other:

1. From the first equation: ( y = -2x + 1 )
2. From the second equation: ( y = 3x – 4 )

Setting them equal to each other:

[

-2x + 1 = 3x – 4

]

Now, let’s solve for ( x ):

1. Add ( 2x ) to both sides:

[

1 = 5x – 4

]

2. Add ( 4 ) to both sides:

[

5 = 5x

]

3. Divide both sides by ( 5 ):

[

x = 1

]

Now substitute ( x = 1 ) back into one of the original equations to find ( y ). I’ll use the first equation:

[

y = -2(1) + 1 = -2 + 1 = -1

]

So, the solution to the system of equations is ( (1, -1) ).

In conclusion, the correct solution is ( (1, -1) ).