Question

-4x-2=-12
4x+8y=-24

Answer 1

Let's solve the system of equations step by step.

**1. Solve the first equation for \( x \)**:

The first equation is:
\[
-4x - 2 = -12
\]

Add 2 to both sides:
\[
-4x = -12 + 2 \\
-4x = -10
\]

Now, divide by -4:
\[
x = \frac{-10}{-4} = \frac{10}{4} = \frac{5}{2}
\]

So, \( x = \frac{5}{2} \).

**2. Substitute \( x \) into the second equation**:

The second equation is:
\[
4x + 8y = -24
\]

Substituting \( x = \frac{5}{2} \):
\[
4\left(\frac{5}{2}\right) + 8y = -24
\]

Calculating \( 4 \times \frac{5}{2} \):
\[
10 + 8y = -24
\]

Now, subtract 10 from both sides:
\[
8y = -24 - 10 \\
8y = -34
\]

Now divide by 8:
\[
y = \frac{-34}{8} = \frac{-17}{4}
\]

So, \( y = \frac{-17}{4} \).

**3. Final solution**:

The solution to the system of equations is:
\[
x = \frac{5}{2}, \quad y = \frac{-17}{4}
\]

You can summarize the solution as \( \left( \frac{5}{2}, \frac{-17}{4} \right) \).