Value of x in pair of linear equations `36x + 24y = 702 and 24x + 36y = 558` is____

Options

A. `(33)/(2)`
B. `(145)/(7)`
C. 16
D. 17

Answer

To find the value of \( x \) in the pair of linear equations:

1. **Given Equations**:
\[ 36x + 24y = 702 \quad (1) \]
\[ 24x + 36y = 558 \quad (2) \]

2. **Multiply the equations to eliminate \( y \)**:
We can multiply the first equation by \( 3 \) and the second equation by \( -2 \) to align the coefficients of \( y \).

- Multiply equation (1) by \( 3 \):
\[ 3(36x + 24y) = 3(702) \]
\[ 108x + 72y = 2106 \quad (3) \]

- Multiply equation (2) by \( -2 \):
\[ -2(24x + 36y) = -2(558) \]
\[ -48x - 72y = -1116 \quad (4) \]

3. **Add equations (3) and (4)**:
\[ (108x + 72y) + (-48x - 72y) = 2106 - 1116 \]
\[ 108x - 48x + 72y - 72y = 2106 - 1116 \]
\[ 60x = 990 \]

4. **Solve for \( x \)**:
\[ x = \frac{990}{60} \]
\[ x = 16.5 \]

Thus, the value of \( x \) is \( 16.5 \).

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