The problem asks to solve the following system of linear equations: $4x - y = 1$ $3x + 4y = 34$ If a unique solution exists, we need to provide the ordered pair $(x, y)$. Otherwise, we should determine if there are infinitely many solutions or no solution.

1. Problem Description

The problem asks to solve the following system of linear equations:

$4x - y = 1$

$3x + 4y = 34$

If a unique solution exists, we need to provide the ordered pair $(x, y)$. Otherwise, we should determine if there are infinitely many solutions or no solution.

2. Solution Steps

We can solve this system of equations using substitution or elimination. Let's use the elimination method.

First, multiply the first equation by 4 to eliminate $y$:

$4(4x - y) = 4(1)$

$16x - 4y = 4$

Now we have the following system:

$16x - 4y = 4$

$3x + 4y = 34$

Add the two equations together:

$(16x - 4y) + (3x + 4y) = 4 + 34$

$19x = 38$

Divide by 19:

$x = \frac{38}{19} = 2$

Now, substitute the value of $x$ back into the first equation $4x - y = 1$ to find $y$:

$4(2) - y = 1$

$8 - y = 1$

$y = 8 - 1 = 7$

So the solution is $x = 2$ and $y = 7$. The ordered pair is $(2, 7)$.

We can check this solution by substituting $x=2$ and $y=7$ into the second equation $3x+4y=34$:

$3(2) + 4(7) = 6 + 28 = 34$, which is correct.

3. Final Answer

A. The solution to the system is $(2, 7)$.