$$ 4 x-3 y=-6 $$ $$ x-7 y=-14 $$ solution

Question

UpStudy AI · Accepted Answer

To solve the system of linear equations:

$$
\begin{cases}
4x - 3y = -6 \quad \quad \quad \text{(1)} \
x - 7y = -14 \quad \quad \text{(2)}
\end{cases}
$$

We can use the **substitution method**. Here's a step-by-step solution:

### Step 1: Solve Equation (2) for $$ x $$

From equation (2):
$$
x - 7y = -14
$$
$$
x = 7y - 14 \quad \quad \text{(3)}
$$

### Step 2: Substitute $$ x $$ from Equation (3) into Equation (1)

Substitute $$ x = 7y - 14 $$ into equation (1):
$$
4(7y - 14) - 3y = -6
$$
$$
28y - 56 - 3y = -6
$$
$$
25y - 56 = -6
$$

### Step 3: Solve for $$ y $$

Add 56 to both sides:
$$
25y = 50
$$
$$
y = \frac{50}{25}
$$
$$
y = 2
$$

### Step 4: Substitute $$ y $$ back into Equation (3) to Find $$ x $$

$$
x = 7(2) - 14
$$
$$
x = 14 - 14
$$
$$
x = 0
$$

### **Solution**

$$
x = 0, \quad y = 2
$$

### **Verification**

To ensure the solution is correct, substitute $$ x = 0 $$ and $$ y = 2 $$ back into both original equations.

1. **Check Equation (1):**
   $$
   4(0) - 3(2) = 0 - 6 = -6 \quad \checkmark
   $$

2. **Check Equation (2):**
   $$
   0 - 7(2) = 0 - 14 = -14 \quad \checkmark
   $$

Both equations are satisfied, confirming that the solution $$ x = 0 $$ and $$ y = 2 $$ is correct.
The solution is $$ x = 0 $$ and $$ y = 2 $$.

\( 4 x-3 y=-6 \) \( x-7 y=-14 \) solution