https://file.aiquickdraw.com/mathbot/file/172876270157431xtlv0s.jpg

The image shows a system of linear equations to solve:

\[
\begin{cases}
5x - 4y = -6 \\
6x - 6y = -5
\end{cases}
\]

Let's solve this system of equations step by step.

### Step 1: Simplify the second equation
We can divide the second equation by 6 to make the coefficients simpler:

\[
x - y = -\frac{5}{6}
\]

### Step 2: Solve for \(x\) in terms of \(y\)
From the simplified second equation:

\[
x = y - \frac{5}{6}
\]

### Step 3: Substitute into the first equation
Substitute \(x = y - \frac{5}{6}\) into the first equation:

\[
5(y - \frac{5}{6}) - 4y = -6
\]

Expanding:

\[
5y - \frac{25}{6} - 4y = -6
\]

Simplify:

\[
y - \frac{25}{6} = -6
\]

### Step 4: Solve for \(y\)
Add \(\frac{25}{6}\) to both sides:

\[
y = -6 + \frac{25}{6} = -\frac{36}{6} + \frac{25}{6} = -\frac{11}{6}
\]

So, \(y = -\frac{11}{6}\).

### Step 5: Solve for \(x\)
Now, substitute \(y = -\frac{11}{6}\) back into \(x = y - \frac{5}{6}\):

\[
x = -\frac{11}{6} - \frac{5}{6} = -\frac{16}{6} = -\frac{8}{3}
\]

### Final Answer:
The solution is \(x = -\frac{8}{3}\) and \(y = -\frac{11}{6}\).

Do you need further details or clarifications?

Here are 5 related questions for further practice:
1. How would you solve a system of equations using substitution?
2. Can you solve a system of equations using elimination?
3. What happens if two equations in a system are parallel?
4. How do you check if the solution to a system of equations is correct?
5. Can you solve a system of equations graphically?

**Tip:** Always try simplifying the equations if possible, as it can make the solution process quicker and easier!

Solve the following system of equations: 5x - 4y = -6, 6x - 6y = -5

Learn how to solve the system of equations 5x - 4y = -6 and 6x - 6y = -5 using the substitution method. This detailed step-by-step solution covers key algebraic concepts like substitution and solving for variables. Suitable for students in Grades 9-11.

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