Solve the system of linear equations using substitution. $$ \begin{array}{l}y=6 x-14 \ y=-8 x \ ext { Solution }\end{array} $$

Question

Solve the system of linear equations using substitution. $$ \begin{array}{l}y=6 x-14 \ y=-8 x \ 	ext { Solution }\end{array} $$

UpStudy AI · Accepted Answer

To solve the system of linear equations using substitution:

$$
\begin{cases}
y = 6x - 14 \quad \text{(Equation 1)} \
y = -8x \quad \text{(Equation 2)}
\end{cases}
$$

**Step 1: Substitute $$ y $$ from Equation 2 into Equation 1.**

Since $$ y = -8x $$ from Equation 2, substitute this into Equation 1:

$$
-8x = 6x - 14
$$

**Step 2: Solve for $$ x $$.**

$$
-8x - 6x = -14 \
-14x = -14 \
x = \frac{-14}{-14} \
x = 1
$$

**Step 3: Substitute $$ x = 1 $$ back into Equation 2 to find $$ y $$.**

$$
y = -8(1) \
y = -8
$$

**Solution:**

$$
x = 1 \quad \text{and} \quad y = -8
$$

**Verification:**

To ensure the solution is correct, substitute $$ x = 1 $$ and $$ y = -8 $$ into both original equations.

- **Equation 1:** $$ y = 6x - 14 $$
  
  $$
  -8 = 6(1) - 14 \
  -8 = 6 - 14 \
  -8 = -8 \quad \text{✓}
  $$

- **Equation 2:** $$ y = -8x $$
  
  $$
  -8 = -8(1) \
  -8 = -8 \quad \text{✓}
  $$

Both equations are satisfied, confirming that the solution is correct.

**Final Answer:**  
$$ x = 1 $$ and $$ y = -8 $$
$$ x = 1 $$ and $$ y = -8 $$.

Solve the system of linear equations using substitution. \( \begin{array}{l}y=6 x-14 \\ y=-8 x \\ \text { Solution }\end{array} \)