Question

Solve the following system by the elimination method.1/3x+y=0/3 and 1/6x+1/5y=9/10

Answer 1

x = 9 and y = -3 → (9, -3)

Explanation:

`\left\{\begin{array}{ccc}(1)/(3)x+y=(0)/(3)&\text{multiply both sides by 3}\\\\(1)/(6)x+(1)/(5)y=(9)/(10)&\text{multiply both sides by 30}\end{array}\right\\[tex]\left\{\begin{array}{ccc}x+3y=0&\text{multiply both sides by (-2)}\\5x+6y=27\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-2x-6y=0\\5x+6y=27\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad3x=27\qquad\text{divide both sides by 3}\\.\qquad\boxed{x=9}\\\\\text{Put the value of x to the first equation:}\\\\9+3y=0\qquad\text{subtract 9 from both sides}\\3y=-9\qquad\text{divide both sides by 3}\\\boxed{y=-3}`[/tex]