Question

3x+5y=6 multiply then add

Answer 1

`\large\boxed{x=-(1)/(2),\ y=(3)/(2)}`

Explanation:

`\left\{\begin{array}{ccc}3x+5y=6&\text{multiply both sides by 4}\\-4x+2y=5&\text{multiply both sides by 3}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}12x+20y=24\\-12x+6y=15\end{array}\right}\qquad\text{add the both sides of the equations}\\.\qquad\qquad26y=39\qquad\text{divide both sides by 26}\\.\qquad\qquad y=(39)/(26)\\.\qquad\qquad y=(39:13)/(26:13)\\.\qquad\qquad\boxed{y=(3)/(2)}\\\\\text{Put the value of y to the second equation}`

`-4x+2\left((3)/(2)\right)=5\\-4x+3=5\qquad\text{subtract 3 from both sides}\\-4x=2\qquad\text{divide both sides by (-4)}\\x=(2)/(-4)\\x=-(2:2)/(4:2)\\\boxed{x=-(1)/(2)}`