[tex] \left \{ {2x + 4y =12} \atop {3x + y = 9}} \right. [/tex]
Think of a number that if you multiply it by the equation would eliminate one variable.
So in this case, I'll use the equation:
3x + y = 9
What number should be multiplied by the equation above that when you combine it with 2x + 4 = 12 would eliminate one variable?
2x + 4y =12
(3x + y = 9) -4 ⇒ -12x - 4y = -36
2x + 4y = 12
-12x - 4y = -36
-----------------------
-10x = -24
-10x -24 24 12
------- = ----- ⇒ x = ----- (lowest term) ⇒ x = ----
-10 -10 10 5
(Now substitute to find y)
2x + 4y = 12
2(12/5) + 4y = 12
24/5 + 4y = 12
I want to remove the fraction part so I'll find for their lcd
(24/5 + 4y = 12) 5
24 + 20y = 60
20y 36 36 9
----- = ---- ⇒ y = ----- ⇒ y = -----
20 20 20 5
CHECK:
3x + y = 9
3(12/5) + 9/5 = 9
36/5 + 9/5 = 9
45/5 = 9
9 = 9
Check the attachment below =)
