How do you solve the following system?: # 2x +4y =-9 , 2x +y = -2#
1 Answer
Mar 15, 2017
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=-# 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]}
