Question

Solve this simultaneous equation.


`x + y = 5 \\ (1)/(x) + (1)/(y) = (9)/(14) \\`

Answer 1

Answer: x∈∅ (there is no decision).

Explanation:

`\left \{ {{x+y=5} \atop {(1)/(x) +(1)/(y)=(9)/(14) }} \right.\ \ \ \ \ \left \{ {{x+y=5} \atop *14*x*y\ (x\\eq 0;\ y\\eq 0) } \right. \ \ \ \ \left \{ {{x+y=5} \atop {14*(x+y)=9*x*y}} \right. \ \ \ \ \left \{ {{x+y=5} \atop {14*5=9*x*y}} \right.\ \ \ \ \left \{ {{x+y=5} \atop {9*x*y=70}} \right. \\`

`\left \{ {{y=5-x} \atop :9} \right. \ \ \ \ \left \{ {{y=5-x} \atop {x*(5-x)=(70)/(9) }} \right.\ \ \ \ \left \{ {{y=5-x} \atop {5x-x^2=(70)/(9) }} \right. \ \ \ \ \left \{ {{y=5-x} \atop x^2-5x+(70)/(9) =0\ } \right.\ \ \ \ \left \{ {{y=5-x} \atop {9x^2-45x+70=0}} \right.`

`\left \{ {{y=5-x} \atop {D=-495}} \right. \ \ \ \ \Rightarrow\ \ \ \ x\in\varnothing.`