To have infinitely many solutions they must describe the same line. So any multiple or fraction of the reference line would indeed describe the same line, and thus "intersect" at each and every of an infinite number of points.

2(x+y=4)

2x+2y=8 (is the same line as x+y=4)

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3 years ago

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OOOO

lbvjy [14]

Step-by-step explanation:

Given bi-quadratic equation is:

$x^4+95x^2 -500=0$

Substituting $x^2=a,$ given bi-quadratic equation reduces in the form of following quadratic equation:

$a^2 +95a -500=0\\$

Let us factorize the above quadratic equation:

$a^2 +95a -500=0\\\therefore\: a^2 +100a -5a-500=0\\\therefore\: a(a +100) -5(a+100)=0\\\therefore\: (a +100)(a -5)=0\\\therefore\: (a +100)=0\:\: or \:\: (a -5)=0\\\therefore\: a = - 100\:\: or \:\: a = 5\\\\CASE\: (1)\:\\When\: a = - 100 \implies x^2 = - 100\\\therefore x=\pm \sqrt{-100}\\$