The image you uploaded contains a system of linear equations. Here are the equations from the image:

1. $-3x + 7y = -16$
2. $-9x + 5y = 16$

Let's solve this system of equations.

Step 1: Use the method of elimination or substitution to solve the system.

Let's solve this by elimination. To eliminate one of the variables, we need to make the coefficients of $x$ or $y$ the same in both equations. We can multiply the first equation by 3 and the second equation by 1 to make the coefficients of $x$ the same.

• Equation 1: $-3x + 7y = -16$ becomes: $(-3x + 7y) \times 3 = -16 \times 3 \implies -9x + 21y = -48$
• Equation 2: $-9x + 5y = 16$ remains the same.

Now we have the system:

1. $-9x + 21y = -48$
2. $-9x + 5y = 16$

Step 2: Subtract the second equation from the first to eliminate $x$:

$(-9x + 21y) - (-9x + 5y) = -48 - 16$ Simplifying:

$-9x + 21y + 9x - 5y = -64 \implies 16y = -64$

Step 3: Solve for $y$:

$y = \frac{-64}{16} = -4$

Step 4: Substitute $y = -4$ into one of the original equations to solve for $x$. Using the first equation:

$-3x + 7(-4) = -16$ $-3x - 28 = -16$ $-3x = -16 + 28 \implies -3x = 12$ $x = \frac{12}{-3} = -4$

Final Answer:

The solution to the system of equations is: $x = -4, \quad y = -4$

Let me know if you would like a more detailed explanation or if you have any further questions!

Here are some follow-up questions:

1. What other methods can be used to solve systems of linear equations?
2. How do you check the solution of a system of equations?
3. What happens if a system of equations has no solution?
4. Can you solve systems of equations involving more than two variables?
5. What is the graphical representation of the solution to a system of linear equations?

Tip: When solving a system of linear equations, always try to choose the method (substitution or elimination) that makes the math simpler.