To solve the system of linear equations:

1. \( 8x + 14y = 4 \)
2. \( -6x - 7y = -10 \)

We can use either substitution or elimination. Here, elimination seems convenient because we can eliminate \( y \) by multiplying the second equation by 2. Let's proceed:

### Step 1: Multiply the second equation by 2 to match the coefficient of \( y \) in both equations.
\[
2(-6x - 7y) = 2(-10)
\]
This gives:
\[
-12x - 14y = -20
\]

### Step 2: Add the two equations to eliminate \( y \):
\[
(8x + 14y) + (-12x - 14y) = 4 + (-20)
\]
\[
(8x - 12x) + (14y - 14y) = -16
\]
\[
-4x = -16
\]

### Step 3: Solve for \( x \):
\[
x = \frac{-16}{-4} = 4
\]

### Step 4: Substitute \( x = 4 \) into one of the original equations (let's use the first equation):
\[
8(4) + 14y = 4
\]
\[
32 + 14y = 4
\]

### Step 5: Solve for \( y \):
\[
14y = 4 - 32
\]
\[
14y = -28
\]
\[
y = \frac{-28}{14} = -2
\]

### Solution:
\[
x = 4, \quad y = -2
\]

Would you like further details or have any questions?

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Here are 5 related questions to explore further:
1. What is the graphical representation of the two equations?
2. How do you solve a system of equations using substitution?
3. Can this system be solved using matrices or determinants?
4. What are some real-life applications of solving systems of equations?
5. What happens if both equations represent the same line?

**Tip:** Always check your solution by substituting the values back into both original equations to verify accuracy.

Learn how to solve the system of linear equations 8x + 14y = 4 and -6x - 7y = -10 using the elimination method. This step-by-step guide demonstrates key algebraic techniques suitable for students in Grades 8-10.

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