Question #4397

x/2 + y/3 = 2/3
x/2 + 2/y = -1
What is the solution of the system?
my school work is online. I can not copy and paste. How would you all be able to help me? There is a possibility of log back in & it being new question...

Expert's answer

x/2 + y/3 = 2/3

x/2 + 2/y =-1

from the first equation we have x/2=2/3 - y/3. Substitute this into the second equation

2/y+2/3 -y/3=-1

2/y-y/3=-5/3

*3y:

y^2-5y-6=0

(y-6)(y+1)=0

y_1=6; y_2=-1

Find the corresponding x=4/3-2y/3

x_1=4/3-2*6/3=-8/3

x_2=4/3-2*(-1)/3=2

Ans: (2,-1),(-8/3,6)

x/2 + 2/y =-1

from the first equation we have x/2=2/3 - y/3. Substitute this into the second equation

2/y+2/3 -y/3=-1

2/y-y/3=-5/3

*3y:

y^2-5y-6=0

(y-6)(y+1)=0

y_1=6; y_2=-1

Find the corresponding x=4/3-2y/3

x_1=4/3-2*6/3=-8/3

x_2=4/3-2*(-1)/3=2

Ans: (2,-1),(-8/3,6)

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