You can put this solution on YOUR website! how do I solve. x-y=4 & x^2-y^2=8
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x-y=4
x^2-y^2=8
(x-y)*(x+y) = 8
4(x+y) = 8
x+y = 2
x-y = 4
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Can you do the rest?
this means that the same solution has to apply to both equations.
your first equation is x-y=4
your second equation is x^2-y^2=8
in the first equation, solve for x to get x = y+4
in the second equation, replace x with y+4 to get (y+4)^2 - y^2 = 8.
(y+4)^2 = y^2 + 8y + 16
(y+4)^2 - y^2 = 8 becomes y^2 + 8y + 16 - y^2 = 8
y^2 on both sides of the equation cancel out and you are left with:
8y+16=8
subtract 16 from both sides of the equation to get:
8y=-8
solve for y to get y = -1
replace y with -1 in the first original equation to get x-y = 4 becomes x-(-1) = 4 which becomes x+1=4.
solve for x to get x = 3.
you have x = 3 and y = -1.
the first original equation of x-y = 4 becomes 3 - (-1) = 4 which becomes 4 = 4, confirming the solution is good for it.
the second original equation of x^2 - y^2 = 8 becomes 3^2 - (-1)^2 = 8 which becomes 9-1=8 which becomes 8 = 8, confirming the solution is good for it.
your solution is confirmed to be good for both original equations and so your solution is that x = 3 and y = -1.
