We need to solve the system of linear equations: $-15x + 7y = 28$ $5x + 6y = 24$

1. Problem Description

We need to solve the system of linear equations:

$-15x + 7y = 28$

$5x + 6y = 24$

2. Solution Steps

We will use the substitution or elimination method to solve for $x$ and $y$. Let's use the elimination method.

Multiply the second equation by $3$ to make the coefficient of $x$ equal to $15$:

$3(5x + 6y) = 3(24)$

$15x + 18y = 72$

Now we have the following system of equations:

$-15x + 7y = 28$

$15x + 18y = 72$

Add the two equations to eliminate $x$:

$(-15x + 7y) + (15x + 18y) = 28 + 72$

$25y = 100$

$y = \frac{100}{25}$

$y = 4$

Now substitute $y = 4$ into the second equation:

$5x + 6(4) = 24$

$5x + 24 = 24$

$5x = 0$

$x = 0$

3. Final Answer

$x=0$ and $y=4$