Question #1a1c4

2 Answers
May 4, 2017

x^2+y^2=26
xy=5

Explanation:

x+y=6 called @
x-y=4 called @@
then @-@@
get 2y=2 so y=1
then x=5
then x^2+y^2=26
xy=5

May 4, 2017

x^2+y^2=26
xy=5

Explanation:

Method 1
Since x+y=6, (x+y)^2=36. Expand the left-hand side to get x^2+2xy+y^2=36.

Since x-y=4, (x-y)^2=16. Expand the left-hand side to get x^2-2xy+y^2=16.

Now, add the first equation to the second equation: (x^2+2xy+y^2)+(x^2-2xy+y^2)=36+16. This gives 2x^2+2y^2=52, or x^2+y^2=26.

Now, subtract the second equation from the first equation: (x^2+2xy+y^2)-(x^2-2xy+y^2)=36-16. This gives 4xy=20, or xy=5.

Method 2
Add x+y=6 to x-y=4 to get (x+y)+(x-y)=6+4, or x=5. Subtract x-y=4 from x+y=6 to get (x+y)-(x-y)=6-4, or y=1.

Thus, x^2+y^2=5^2+1^2=26 and xy=5*1=5.