Question

the solutions for pair of equations..........??
1/16x +1/15y = 9/20
1/20x - 1/27y = 4/25

Answer 1

$$\left\{ \begin{array}{l} \frac {1}{16} x + \frac {1}{15} y = \frac {9}{20} \\ \frac {1}{20} x - \frac {1}{27} y = \frac {4}{25} \end{array} \right.$$

Solution.

Subtract $\left(4 / 5 \times \text{equation 1}\right)$ from equation 2:

$$\left\{ \begin{array}{l} \frac {1}{16} x + \frac {1}{15} y = \frac {9}{20} \\ 0x - \frac {61}{675} y = - \frac {1}{5} \end{array} \right.$$

Multiply equation 1 by 240:

$$\left\{ \begin{array}{l} 15x + 16y = 108 \\ 0x - \frac {61}{675} y = - \frac {1}{5} \end{array} \right.$$

Multiply equation 2 by -675:

$$\left\{ \begin{array}{l} 15x + 16y = 108 \\ 61y = 135 \end{array} \right.$$

Swap the equations and find $y$:

$$\left\{ \begin{array}{c} y = \frac {135}{61} \\ 15x + 16y = 108 \end{array} \right.$$

Substitute $y$ into second equation:

$$\left\{ \begin{array}{c} y = \frac {135}{61} \\ 15x + 16 \cdot \frac {135}{61} = 108 \end{array} \right.$$

Find $x$:

$$\left\{ \begin{array}{l} y = \frac {135}{61} \\ 15x = \frac {4428}{61} \end{array} \right.$$ $$\left\{ \begin{array}{l} y = \frac {135}{61} \\ x = \frac {1476}{305} \end{array} \right.$$

Answer:

$$\left(\frac {1476}{305}, \frac {135}{61}\right)$$