Mathematics: Solve the system of equations {x−4y=3 2x+y=−3} write your answers as an ordered pair.

Solve the system of equations {x−4y=3 2x+y=−3} write

Ответ:

darianhaynes

09.03.2022

(-1, -1)

Step-by-step explanation:

$Substitution\ method:\\\\\left\{\begin{array}{ccc}x-4y=3&\text{add 4y to both sides}\\2x+y=-3\end{array}\right\\\\\left\{\begin{array}{ccc}x=4y+3\\2x+y=-3\end{array}\right\\\\\text{Substitute from the first equation to the second equation:}\\\\2(4y+3)+y=-3\qquad\text{use distributive property}\\\\(2)(4y)+(2)(3)+y=-3\\\\8y+6+y=-3\qquad\text{subtract 6 from both sides}\\\\9y=-9\qquad\text{divide both sides by 9}\\\\\boxed{y=-1}\\\\\text{Put the value of y to the first equation:}\\\\x=4(-1)+3\\\\x=-4+3\\\\\boxed{x=-1}\\\\\boxed{\boxed{x=-1,\ y=-1\to(-1,\ -1)}}$

$Elimination\ method:\\\\\left\{\begin{array}{ccc}x-4y=3\\2x+y=-3&\text{multiply both sides by 4}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}x-4y=3\\8x+4y=-12\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad9x=-9\qquad\text{divide both sides by 9}\\.\qquad\qquad\boxed{x=-1}\\\\\text{Put the value of x to the first equation:}\\\\-1-4y=3\qquad\text{add 1 to both sides}\\\\-4y=4\qquad\text{divide both sides by (-4)}\\\\\boxed{y=-1}\\\\\boxed{\boxed{x=-1,\ y=-1\to(-1,\ -1)}}$