How do you solve 2x+y=02x+y=0 and x-y=1x−y=1 using substitution?

2 Answers
EZ as pi
Jun 16, 2016

x =1/3 and y = -2/3x=13andy=−23

Explanation:

Write one of the equations with a single variable as the subject.
This could be :
y = -2x " or " x = 1 + y " or " y = x-1y=−2x or x=1+y or y=x−1

I would use the fact that both equations can be written with y as the subject.

As y = yy=y it follows that

x - 1 = -2xx−1=−2x
" "3x = 1 3x=1

x = 1/3x=13

Now that we know the value of xx, substitute into one of the equations to find the value for yy

y = -2 xx 1/3 = -2/3y=−2×13=−23

SagarStudy
Jun 16, 2016

2x+y=0.......(i)
x-y=1.........(ii)

From (ii) put y=x-1 in (i).

2x+(x-1)=0
implies 3x=1
implies x=1/3

Now,put x=1/3 in either (i) or (ii) to find the value of y. I am going to put x=1/3 in (i) but you can put in (ii) for practice.

2(1/3)+y=0
implies y=-2/3

Solution Set={(1/3,-2/3)}

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