The line 5x + 4y = 0 passes through the point of intersection of straight lines (1) x+2y-10 = 0, 2x + y =-5

Answer

True

Explanation

Given that,
`x+2y-10=0`.......(i)
and `2x+y+5=0` ......(ii)
From Eq. (i), put the value of `x=10-2y` in Eq. (ii), we get
`20-4y+y5=0`
`rArr 20-3y+5=0`
`y=(25)/(3)`
`becausex+(50)/(3)-10=0`
`rArrx+(20)/(3)=0rArrx=(-20)/(3)` [using Eq. (i)]
So,the point intersection is `((20)/(3),(25)/(3))`
If the line `5x+4y=0` passes through the point `(-(20)/(3),(25)/(3))` then this should lie on this line.
`therefore 5((-20)/(3))+(4(25))/(3)=(-100)/(3)+(100)/(3)=0`
So, this point lies on the given line. Hence, the statements is true.