Question

Solve the system algebraically 5 x - y = 0

Answer 1

To solve the system of equations,

`\begin{gathered} 5x-y=0 \\ (y^2)/(90)-(x^2)/(36)=1 \end{gathered}`

Solving 1st equation we get,

`y=5x`
`(y^2)/(90)-(x^2)/(36)=1`

Substitute y=5x in the above equation, we get

`((5x)^2)/(90)-(x^2)/(36)=1`
`(25x^2)/(90)-(x^2)/(36)=1`
`(5x^2)/(18)-(x^2)/(36)=1`
`(10x^2-x^2)/(36)=1`
`(9x^2)/(36)=1`
`(x^2)/(4)=1`
`x^2=4`
`x=\pm2`

when x=2, we get y=5x=5(2)=10

when x=-2, we get y=5x=5(-2)=-10

There are two solution for the given system.

`(2,10),(2,-10)`

Answer is: x=2,y=10 and x=2,y=-10