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adelina 88 [10]
4 years ago
11

Please help i'm not that good at math. Determine the number of real solutions for each system of equations.

Mathematics
2 answers:
ratelena [41]4 years ago
7 0

System A has ONE real solution

System B has NO real solutions

System C has ONE real solution

timurjin [86]4 years ago
5 0

A is a circle around the origin and a line through the origin, so they'll intersect in two places; we can skip the detailed calculation.

B is the intersection of a parabola and a line; they can intersect in zero, one or two places depending on the details. Let's check

y=x^2-7x+10=-6x+5

x^2-x+5= 0

Discriminant,

d = b^2-4ac=1-(4)(5)=-19

Negative discriminant, zero real solutions for B.

System C is again a parabola and a line; we proceed similarly:

y = 8x+17 = -2x^2+9

2x^2+8x+8=0

x^2 + 4x + 4 = 0

d=b^2-4ac=16 - 4(1)(4)=0

Zero discriminant, exactly one real solution for C.

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