Question

If x + y = 5 and xy = 10, what are the value of x^ and y^?

Answer 1

x, y={7 1/2, -5/2}

PREMISES

x, y={ }, if x+y=5 and x-y=10

Sufficient Conditions:

x+y=5 and x-y=10 (a system of equations)

CALCULATIONS

(x-y=10)-(x+y=5)

0x-2y=5

-2y=5

-2y/-2=5/-2

y=

-5/2 or -2 1/2 or -2.5

And, if y=-5/2, then by substitution,

x+y=5

x+(-5/2)=5

x+(-5/2+5/2)=5+(5/2)

x+0=5+(5/2) (Convert 5/2 to the mixed fraction 2 1/2 to make the math easier)

x=5+(2 1/2)(

x=

7 1/2 or 15/2 or 7.5

PROOF

If x, y={7 1/2, -5/2}, then the equations

(x-y=10)-(x+y=5) becomes

[(7 1/2)-(-5/2)]-[(7 1/2)+(-5/2)]=10–5

[(7 1/2)+(5/2)]-[(7 1/2)-(5/2)]=10–5

10–5=10–5 and

5=5 establish the roots (zeroes) x, y={7 1/2, -5/2} of the compound statement x+y=5, x-y=10 in the premises above

Answer 2

Step-by-step explanation:

step by step solution in photo