Let me analyze the image to extract the mathematical problem and solve it. One moment, please.The system of equations provided in the image is:

$-3x + 5y = 21$ $6x - y = -15$

Let us solve this step by step.

Step 1: Solve for $y$ in terms of $x$ from the second equation

$6x - y = -15$ Rearranging: $y = 6x + 15$

Step 2: Substitute $y = 6x + 15$ into the first equation

Substitute into $-3x + 5y = 21$: $-3x + 5(6x + 15) = 21$

Simplify: $-3x + 30x + 75 = 21$ $27x + 75 = 21$

Solve for $x$: $27x = 21 - 75$ $27x = -54$ $x = -2$

Step 3: Substitute $x = -2$ into $y = 6x + 15$

$y = 6(-2) + 15$ $y = -12 + 15$ $y = 3$

Solution:

The solution to the system of equations is: $\boxed{(-2, 3)}$

Let me know if you'd like further explanation!

Related Questions:

1. How do you solve a system of equations graphically?
2. What are alternative methods to solve systems of equations, such as elimination?
3. Can you solve systems of equations using matrices?
4. What are real-world applications of systems of equations?
5. How do you identify if a system of equations has no solution or infinitely many solutions?

Tip:

Always double-check your solution by substituting it back into the original equations!