How do you solve #y=x^2, y=-2x-1# using substitution?

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Answer 1 · 2017-09-10T19:10:21

#(x,y)=(-1,1).# graph{(y-x^2)(y+2x+1)=0 [-10, 10, -5, 5]}

Let, #y=x^2......(1), and, y=-2x-1......(2).#

Sub.ing #y# from #(1)# in #(2),# we get,

#x^2=-2x-1, or, x^2+2x+1=0.#

# :. (x+1)^2=0.#

#:. x=-1, and,"by "(1)," then, "y=x^2=(-1)^2=1.#

Hence, the Soln. is, #(x,y)=(-1,1).#

N.B. : Geometrically, the Line #y=-2x-1# is tangent to the

Parabola #y=x^2.#

Enjoy Maths!