8x+4y=
20
minus, 4, x, minus, y, equals, minus, 15
−4x−y=
−15

To solve the system of equations:

\[
8x + 4y = 20
\]
\[
-4x - y = -15
\]

we can use either substitution or elimination. Let's go through the elimination method here.

### Step 1: Simplify the system
The system is:
1. \(8x + 4y = 20\)
2. \(-4x - y = -15\)

To simplify, let's multiply the second equation by \(4\) to make the coefficients of \(y\) the same in both equations:

\[
-4 \times (-4x - y) = -4 \times (-15)
\]
giving
\[
-16x - 4y = 60
\]

So our updated system is:
1. \(8x + 4y = 20\)
2. \(-16x - 4y = 60\)

### Step 2: Add the equations
Now, add the two equations together to eliminate \(y\):
\[
(8x + 4y) + (-16x - 4y) = 20 + 60
\]
This simplifies to:
\[
-8x = 80
\]

### Step 3: Solve for \(x\)
Now, divide by \(-8\) to isolate \(x\):
\[
x = -10
\]

### Step 4: Substitute \(x\) back to find \(y\)
Now, substitute \(x = -10\) back into one of the original equations. Using the first equation:
\[
8(-10) + 4y = 20
\]
\[
-80 + 4y = 20
\]
Add 80 to both sides:
\[
4y = 100
\]
Now, divide by 4:
\[
y = 25
\]

### Solution
The solution to the system is:
\[
x = -10, \quad y = 25
\]

Would you like more details or have any questions?

---

Here are some related questions to explore:

1. How do substitution and elimination methods differ in solving systems of equations?
2. How can we verify the solution of a system of equations?
3. What is the graphical interpretation of solving a system of two linear equations?
4. What are some common applications of systems of equations?
5. How do we handle systems of equations with no solution or infinitely many solutions?

**Tip:** Always check your solution by plugging the values back into the original equations to confirm they satisfy both.

Solve the system of equations: 8x + 4y = 20 and -4x - y = -15

Master solving the system of equations 8x + 4y = 20 and -4x - y = -15 using the elimination method. This step-by-step guide explores key algebraic concepts and provides detailed solutions, ideal for students in Grades 8-10.

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