Question

The first equation of the system is multiplied by 4. By what number would you multiply the second equation in order to eliminate the x variable by adding?

3x-2y=4
4x+5y=28

Answer 1

Since you've multiplied the firs equation by 4 you have a 12x. So you must found a number that multiplied by the 4x in the second equation will result in -12x. Concerning that the negative signal turns the number to negative, you come to the answer -3 (Minus three)

Answer 2

`\left \{ {3x-2y=4\ \ \ \atop {4x+5y=28}} \right. \\\\ \left \{ {{12x-8y=16} \atop {4x+5y=28}} \right.\\\\To\ eliminate\ by\ adding\ multiply\ second\ equation\ by\ -3\ to\\ obtain\ -12x\\\\ \left \{ {{12x-8y=16} \atop {-12x-15y=-84}} \right.\\+----\\Addition:\\\\ -8y-15y=16-84\\ -33y=-68\\ y=(68)/(33)\\ 4x=28-5y\\ x=(28-5y)/(4)=(28-5*(68)/(33))/(4)=(1)/(4)`