Question

$1) \left \{ {{x/2+2x=10} \atop {x+y=6}} \right. 2) \left \{ {{2x/3-3y/2=1} \atop {x+y=4}} \right.$

Answer 1

1)

x/2 + 2x = 10
(x + 4x)/2 = 10
5x = 20
x = 4

x + y = 6
5 + y = 6
y = 1

2)

2x/3 - 3y/2 = 1
(2x - 9y)/6 =1
2x - 9y = 6
2x = 6 + 9y
x = (6 + 9y)/2

x + y = 4
(6 + 9y)/2 + y = 4
(6 + 9y + 2y)/2 = 4
6 + 11y = 8y
6 = - 3y
- 2 = y

x = (6 + 9y)/2
x = (6 + 9(- 2))/2
x = (6 + (- 18))/2
x = - 6