Question

36x+45y=123
46x+15y=23

Answer 1

Elimination Method

`\left\{\begin{array}{ccc}36x+45y=123&\text{divide both sides by (-3)}\\46x+15y=23\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-12x-15y=-41\\46x+15y=23\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad34x=-18\qquad\text{divide both sides by 34}\\.\qquad\qquad x=-(18)/(34)\to\boxed{x=-(9)/(17)}\\\\\text{Put the value of x to the second equation.}\\\\46\left(-(9)/(17)\right)+15y=23`

`-(414)/(17)+15y=(391)/(17)\qquad\text{add}\ (414)/(17)\ \text{to both sides}\\\\15y=(805)/(17)\qquad\text{divide both sides by}\ 15\\\\y=(805)/(255)\\\\\boxed{y=(161)/(51)}\\\\Answer:\ \boxed{x=-(9)/(17)\ and\ y=(161)/(51)}`