Question

−8x+4y=0
-x +2y = -9
solve by elimanation

Answer 1

To solve the system of equations using the elimination method, we start with the two equations:

1) \( -8x + 4y = 0 \)
2) \( -x + 2y = -9 \)

**Step 1: Align the equations for elimination.**

We can make the second equation consistent with the first by multiplying it by 4, so that the coefficients of \(y\) match.

\[
4(-x + 2y) = 4(-9)
\]

This gives us:

\[
-4x + 8y = -36 \quad \text{(Equation 3)}
\]

Now we have:

1) \( -8x + 4y = 0 \)
3) \( -4x + 8y = -36 \)

**Step 2: Eliminate one variable.**

We can multiply Equation 1 by 2 to line it up with Equation 3:

\[
2(-8x + 4y) = 2(0)
\]
This simplifies to:

\[
-16x + 8y = 0 \quad \text{(Equation 4)}
\]

Now we have:

4) \( -16x + 8y = 0 \)
3) \( -4x + 8y = -36 \)

**Step 3: Subtract Equation 3 from Equation 4.**

Now we can eliminate \(y\) by subtracting:

\[
(-16x + 8y) - (-4x + 8y) = 0 - (-36)
\]

This simplifies to:

\[
-16x + 4x = 36
\]
\[
-12x = 36
\]

**Step 4: Solve for \(x\).**

Divide both sides by \(-12\):

\[
x = \frac{36}{-12} = -3
\]

**Step 5: Substitute \(x\) back to solve for \(y\).**

Now we substitute \(x = -3\) back into one of the original equations. We'll use the second equation \( -x + 2y = -9 \):

\[
-(-3) + 2y = -9
\]
\[
3 + 2y = -9
\]
\[
2y = -9 - 3
\]
\[
2y = -12
\]
\[
y = \frac{-12}{2} = -6
\]

**Solution:**

The solution to the system of equations is:

\[
x = -3, \quad y = -6
\]

Thus, the solution is \( (x, y) = (-3, -6) \).