Let's solve the given system of equations by combining the equations:

Equations:

1. $5x + 6y = -3$
2. $8x + 8y = 8$

Step 1: Eliminate one variable

To eliminate one variable, we'll multiply the equations to align the coefficients of either $x$ or $y$.

Let's eliminate $y$ by making the coefficients of $y$ in both equations equal. We can do this by multiplying the first equation by $4$ and the second equation by $3$ to make the coefficients of $y$ equal to $24$:

• Multiply the first equation by $4$: $4(5x + 6y) = 4(-3) \implies 20x + 24y = -12$

• Multiply the second equation by $3$: $3(8x + 8y) = 3(8) \implies 24x + 24y = 24$

Step 2: Subtract the equations

Now subtract the first equation from the second to eliminate $y$:

$(24x + 24y) - (20x + 24y) = 24 - (-12)$ $(24x - 20x) = 36$ $4x = 36$ $x = 9$

Step 3: Substitute $x = 9$ into one of the original equations

Substitute $x = 9$ into the first equation:

$5x + 6y = -3$ $5(9) + 6y = -3$ $45 + 6y = -3$ $6y = -3 - 45$ $6y = -48$ $y = -8$

Solution:

The solution to the system of equations is: $x = 9, \, y = -8$

Would you like more details or have any questions?

Here are some related questions:

1. How do you solve a system of equations using the substitution method?
2. What are the different methods to solve a system of linear equations?
3. Can systems of linear equations have no solution or infinitely many solutions?
4. How can you verify the solution to a system of equations?
5. What are the applications of solving systems of equations in real-world problems?

Tip: Always check your solution by substituting the values of $x$ and $y$ back into the original equations to ensure they satisfy both equations.