Solve, using cross - multiplication :
5x + 4y + 14 = 0
3 = - 10 - 4y

Answer

To solve the given simultaneous equations using cross-multiplication, we will follow these steps:

### Step 1: Write the equations in standard form
We have the two equations:
1. \( 5x + 4y + 14 = 0 \)
2. \( 3 = -10 - 4y \)

First, we will rearrange the second equation to standard form:
\[ 3 + 10 + 4y = 0 \implies 4y + 13 = 0 \]
Thus, the two equations are:
1. \( 5x + 4y + 14 = 0 \)
2. \( 4y + 13 = 0 \)

### Step 2: Identify coefficients
From the equations, we can identify the coefficients:
- For the first equation \( a_1 = 5, b_1 = 4, c_1 = 14 \)
- For the second equation \( a_2 = 0, b_2 = 4, c_2 = 13 \)

### Step 3: Apply the cross-multiplication formula
The formulas for \( x \) and \( y \) in cross-multiplication are:
\[ x = \frac{b_1 c_2 - b_2 c_1}{a_1 b_2 - a_2 b_1} \]
\[ y = \frac{c_1 a_2 - c_2 a_1}{a_1 b_2 - a_2 b_1} \]

### Step 4: Substitute the values into the formulas
Substituting the values we identified:
\[ x = \frac{4 \cdot 13 - 4 \cdot 14}{5 \cdot 4 - 0 \cdot 4} \]
\[ y = \frac{14 \cdot 0 - 13 \cdot 5}{5 \cdot 4 - 0 \cdot 4} \]

### Step 5: Simplify the equations
Now, we simplify:
1. For \( x \):
\[ x = \frac{52 - 56}{20 - 0} = \frac{-4}{20} = -\frac{1}{5} \]

2. For \( y \):
\[ y = \frac{0 - 65}{20 - 0} = \frac{-65}{20} = -\frac{13}{4} \]

### Step 6: Final values
Thus, the solution to the simultaneous equations is:
\[ x = -\frac{1}{5}, \quad y = -\frac{13}{4} \]