https://file.aiquickdraw.com/mathbot/file/172987228114993x8hwb1.jpg

The system of equations shown in your image is:

\[
\begin{aligned}
1) \quad 5x - 4y &= 19 \\
2) \quad 4x + 3y &= 9
\end{aligned}
\]

We will solve this using the elimination method. Here are the steps:

### Step 1: Multiply both equations to make the coefficients of one variable opposites.

Let's eliminate \(x\). To do that, we need to equalize the coefficients of \(x\). We can multiply the first equation by 4 and the second equation by 5:

\[
\text{Multiply Eq (1) by 4: } 4(5x - 4y) = 4(19) \implies 20x - 16y = 76
\]
\[
\text{Multiply Eq (2) by 5: } 5(4x + 3y) = 5(9) \implies 20x + 15y = 45
\]

### Step 2: Subtract the two equations.

Now, subtract the second equation from the first to eliminate \(x\):

\[
(20x - 16y) - (20x + 15y) = 76 - 45
\]
\[
20x - 20x - 16y - 15y = 31
\]
\[
-31y = 31
\]

### Step 3: Solve for \(y\).

\[
y = \frac{31}{-31} = -1
\]

### Step 4: Substitute \(y = -1\) into one of the original equations.

Let's substitute \(y = -1\) into the first equation \(5x - 4y = 19\):

\[
5x - 4(-1) = 19
\]
\[
5x + 4 = 19
\]
\[
5x = 15
\]
\[
x = \frac{15}{5} = 3
\]

### Final Solution:

The solution to the system is:

\[
(x, y) = (3, -1)
\]

Let me know if you'd like any more details or if you have any questions!

---

Here are 5 related questions to expand your understanding:

1. How do you solve a system of equations using substitution instead of elimination?
2. Can the elimination method always be applied to a system of two equations?
3. What happens if the two lines represented by the equations are parallel?
4. How can you verify if your solution to a system of equations is correct?
5. What other methods are used to solve systems of equations?

**Tip:** When using the elimination method, always check for the simplest variable to eliminate first to save time.

Solve the system of linear equations using elimination: 5x - 4y = 19 and 4x + 3y = 9.

Learn how to solve the system of linear equations 5x - 4y = 19 and 4x + 3y = 9 using the elimination method. This step-by-step guide covers key algebraic concepts and is suitable for students in Grades 8-10.

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