Value of x = 0 or 1 and value of y = [tex]\frac{-3}{2}[/tex] or -1 for the given quadratic equation.
" Quadratic equation is defined as the polynomial whose highest degree of the given variable is equals to 2."
According to the question,
Given equations,
[tex]x-2y=3[/tex]
⇒[tex]x=3 + 2y[/tex] ____(1)
Quadratic equation,
[tex]3x^{2} -5xy-16y=24[/tex] ____(2)
Substitute the value of 'x' from (1) in (2) quadratic equation we get,
[tex]3(3+2y)^{2} -5(3+2y)y-16y=24[/tex]
⇒[tex]3(9+12y+4y^{2} )-5y(3+2y) -16y-24=0[/tex]
⇒[tex]27+36y+12y^{2} -15y-10y^{2} -16y-24=0[/tex]
⇒[tex]2y^{2} +5y+3=0[/tex]
⇒[tex]2y^{2} +2y+3y+3=0[/tex]
⇒[tex]2y(y+1)+3(y+1)=0[/tex]
⇒[tex](2y+3)(y+1)=0[/tex]
⇒[tex](2y+3)=0 or (y+1)=0[/tex]
⇒[tex]y=\frac{-3}{2} or y = -1[/tex]
Substitute in (1) to get the value of 'x' ,
[tex]x= 3+ 2(\frac{-3}{2}) or x = 3 + 2 (-1)[/tex]
⇒ [tex]x = 0 or x = 1[/tex]
Hence, value of x = 0 or 1 and value of y = [tex]\frac{-3}{2}[/tex] or -1 for the given quadratic equation.
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