The problem asks us to solve the following system of linear equations: $3x - y = 17$ $x + 4y = 10$

1. Problem Description

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

$3x - y = 17$

$x + 4y = 10$

2. Solution Steps

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

Multiply the second equation by -3 to eliminate the $x$ variable.

$-3(x + 4y) = -3(10)$

$-3x - 12y = -30$

Now we have the system:

$3x - y = 17$

$-3x - 12y = -30$

Add the two equations:

$(3x - y) + (-3x - 12y) = 17 + (-30)$

$3x - y - 3x - 12y = -13$

$-13y = -13$

Divide both sides by -13:

$y = \frac{-13}{-13}$

$y = 1$

Now that we have the value of $y$, we can substitute it back into either of the original equations to solve for $x$. Let's use the second equation:

$x + 4y = 10$

$x + 4(1) = 10$

$x + 4 = 10$

$x = 10 - 4$

$x = 6$

Therefore, the solution is $x = 6$ and $y = 1$.

3. Final Answer

$x = 6, y = 1$

(6, 1)