Question

Solve the system of equations {x−4y=3

2x+y=−3}
Write your answers as an ordered pair.

Answer 1

-1/3, 5/3

Explanation:

Isolate x for x: -4y=3 x=3+4y

Substitute: x=3+4y

(2(3+4y)+y=3)

Isolate y for: 2(3+4y)+y=3 y=-1/3

Substitute: y=-1/3

3+4(-1/3)

3+4(-1/3)=5/3

x=5/3

-1/3,5/3

Answer 2

(-1, -1)

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)}}`