How do you solve $y=x^2$ and $y=1/2x+5$ using substitution?

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Answer 1 · 2017-06-30T11:03:51

Solution: $( x= 5/2 , y= 25/4) or (x= -2 , y=4)$

$y= x^2 (1) and y =1/2 x +5 (2)$ . Substituting $y =1/2 x +5$ in equation (1) we get,

$x^2 =1/2 x +5 or 2x^2 =x+10 or 2x^2 -x -10 = 0$ or

$2x^2 -5x +4x -10 = 0 or x(2x-5) + 2(2x-5) =0$ or

$(2x-5)(x+2) = 0$ . Either $2x-5 = 0 or 2x= 5 :. x=5/2$ or

$x+2=0 :. x=-2 :. x =5/2 or x= -2$

When $x=5/2 ; y= 1/2*5/2 +5 = 5/4+5 =25/4$ ;

When $x=-2 ; y= 1/2*(-2) +5 = -1+5 =4$ ;

Solution: $( x= 5/2 , y= 25/4) or (x= -2 , y=4)$ [Ans]

How do you solve y=x^2y=x^2 and y=1/2x+5y=1/2x+5 using substitution?