How do you solve the following system?: # 2x +4y =-9 , 2x +y = -2#

1 Answer
Mar 15, 2017

Answer:

#(1/6,-7/3)#

Explanation:

Labelling the equations.

#color(red)(2x)+4y=-9to(1)#

#color(red)(2x)+y=-2to(2)#

Notice that the term #color(red)(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"#

#(color(red)(2x-2x))+(4y-y)=(-9-(-2))#

#rArr3y=-#7

divide 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]}