Question

a) {x-y=10

     {2x=3y=10

 

b) {x+y=3

     {12x-9y= -20

 

c) {2x+y=7

    {5x-2y=5

 

d) {x=5y

     {x+y=12

 

e) {x-y=4

     {2x-4y=13

Answer 1

a)$\left \{ {{x - y = 10} \atop {2x + 3y =10}} \right.$
$x = 10 + y$
$3y = 10 - 2x$
$3y = 10 - 2(10 + y)$
$3y = 10 - 20 - 2y$
$5y = - 10$
                               $y = - 2$
$x = 10 - 2$
                                 $x = 8$


b) $\left \{ {{x + y = 3} \atop {12x - 9y = - 20}} \right.$
$y = 3 - x$
$12x = 9y - 20$
$12x = 9(3 - x) - 20$
$12x = 27 - 9x - 20$
$21x = 7$
                              $x = \frac{1}{3}$
$y = 3 - \frac{1}{3}$
$3y = 9 - 1$
                              $y = \frac{8}{3}$

c)$\left \{ {{2x + y = 7} \atop {5x - 2y = 5}} \right$
$y = 7 - 2x$
$5x = 5 + 2y$
$5x = 5 + 2(7 - 2x)$
$5x = 5 + 14 - 4x$
$9x = 19$
                                      $x = \frac{19}{9}$
$y = 7 - 2( \frac{19}{9} )$
$y = 7 - \frac{38}{9}$
$9y = 63 - 38$
                                      $y = \frac{25}{9}$

d)$\left \{ {{x = 5y} \atop {x + y = 12}} \right.$
$x = 5y$
$y = 12 - x$
$y = 12 - (5y)$
$6y = 12$
                                 $y = 2$
$x = 5 (2)$
                                 $x = 10$

e)$\left \{ {{x - y = 4} \atop {2x - 4y = 13}} \right.$
$- y = 4 - x$
$y = x - 4$
$2x = 13 + 4y$
$2x = 13 + 4(x - 4)$
$2x = 13 + 4x - 16$
$- 2x = - 3$
                                      $x = \frac{3}{2}$
$y = \frac{3}{2} - 4$
$2x = 3 - 8$
$2x = - 5$
                                      $x = - \frac{5}{2}$