To solve the system of equations using the elimination method, follow these steps:
1. **Write down the system of equations:**
\( x + 2y = -6 \)
\( 3x + 8y = -20 \)
2. **Align the equations for elimination:**
Let's multiply the first equation by 3 so that the coefficients of \( x \) in both equations become the same:
\( 3(x + 2y) = 3(-6) \)
This simplifies to:
\( 3x + 6y = -18 \)
Now, the system looks like this:
\( 3x + 6y = -18 \)
\( 3x + 8y = -20 \)
3. **Subtract the first equation from the second:**
\( (3x + 8y) - (3x + 6y) = -20 - (-18) \)
This simplifies to:
\( 3x + 8y - 3x - 6y = -20 + 18 \)
\( 2y = -2 \)
4. **Solve for \( y \):**
\( y = \frac{-2}{2} \)
\( y = -1 \)
5. **Substitute \( y \) back into one of the original equations to solve for \( x \):**
Use the first equation \( x + 2y = -6 \):
\( x + 2(-1) = -6 \)
\( x - 2 = -6 \)
\( x = -6 + 2 \)
\( x = -4 \)
So, the solution to the system of equations is:
\[ (x, y) = (-4, -1) \]
Therefore, the correct answer is \((–4, –1)\).
15.
Solve the system using elimination.
x + 2y = –6
3x + 8y = –20
(–1, –4)
(–4, 4)
(–4, –1)
(3, 1)
1 answer