How do you solve the following system?: 2x +4y =-9 , 2x +y = -22x+4y=−9,2x+y=−2
1 Answer
Mar 15, 2017
Explanation:
Labelling the equations.
color(red)(2x)+4y=-9to(1)2x+4y=−9→(1)
color(red)(2x)+y=-2to(2)2x+y=−2→(2) Notice that the term
color(red)(2x)2x is common to both equations.Thus, subtracting (2) from (1) will eliminate it leaving an equation in y which we can solve.
"Subtract "(1)-(2)" term by term"Subtract (1)−(2) term by term
(color(red)(2x-2x))+(4y-y)=(-9-(-2))(2x−2x)+(4y−y)=(−9−(−2))
rArr3y=-⇒3y=− 7divide both sides by 3
(cancel(3) y)/(cancel(3))=(-7)/3
rArry=-7/3 Substitute this value into either (1) or (2) and solve for x
Substituting in ( 2)
2x-7/3=-2
rArr2x=-2+7/3=1/3 dividing both sides by 2
(cancel(2) x)/cancel(2)=(1/3)/2
rArrx=1/3xx1/2=1/6
rArr(1/6,-7/3)" is the solution"
graph{(y+2x+2)(y+1/2x+9/4)=0 [-12.66, 12.65, -6.33, 6.33]}
