What is the answer? Use elimination or substitution to solve -5x+14y=17" "and" "9x-6y=27

Mar 15, 2018

$x = 5 \mathmr{and} y = 3$

Explanation:

Let the equations be:
$- 5 x + 14 y - 17 = 0 \text{ }$(be equation 1)
$\text{ "9x-6y-27=0" }$ (be equation 2)

(equation 1 implies)=> $14 y = 5 x + 17$

=> $\text{ } y = \frac{5 x + 17}{14}$ (be equation 3)

(Substitute into equation 2 )

$9 x - 6 \left\{\frac{5 x + 17}{14}\right\} - 27 = 0 \text{ } \leftarrow \times 14$

=> $126 x - 30 x - 102 - 378 = 0$

=> $96 x - 480 = 0$

=> $96 x = 480$

=> $x = \frac{480}{96}$

=> $x = 5$

Now, substitute into equation 3

=> $y = \frac{5 \left(5\right) + 17}{14} \text{ }$(taking x=5)

=> $y = \frac{\left(25\right) + 17}{14}$

=> $y = \frac{42}{14}$

$y = 3$

Mar 15, 2018

$y = 3 , x = 5$

Explanation:

$\therefore - 5 x + 14 y = 17 - - - - - - - - - \left(1\right)$

$\therefore 9 x - 6 y = 27 - - - - - - - - - - - \left(2\right)$

$\therefore \left(1\right) \times 9$

$\therefore - 45 x + 126 y = 153 - - - - - - \left(3\right)$

$\therefore \left(2\right) \times 5$

$\therefore 45 x - 30 y = 135 - - - - - - - \left(4\right)$

$\therefore \left(3\right) + \left(4\right)$

$\therefore 96 y = 288$

$\therefore y = 3$

substitute $y = 3$ in$\left(2\right)$

$\therefore 9 x - 6 \left(3\right) = 27$

$\therefore 9 x - 18 = 27$

$\therefore 9 x = 27 + 18$

$\therefore 9 x = 45$

$\therefore x = 5$

~~~~~~~~~

check:-

Substitute $y = 3$and $x = 5$ in $\left(2\right)$

$\therefore 9 \left(5\right) - 6 \left(3\right) = 27$

$\therefore 45 - 18 = 27$

$\therefore 27 = 27$