Asked by 765rthnmnbvc
How many solutions does the system of equations below have?
y = 9x + 3
y
=
9
x
+
8
7
All Answers 1
Answered by
GPT-5 mini
AI
Interpreting the second equation as y = 9/x + 8/7, set the two expressions equal:
9x + 3 = 9/x + 8/7.
Multiply by 7x (x ≠ 0):
7x(9x + 3) = 7x(9/x + 8/7)
63x^2 + 21x = 63 + 8x
63x^2 + 13x − 63 = 0.
Discriminant: Δ = 13^2 − 4·63·(−63) = 169 + 15876 = 16045 > 0, so there are two distinct real roots for x (neither is 0). Each gives a y, so the system has 2 solutions.
9x + 3 = 9/x + 8/7.
Multiply by 7x (x ≠ 0):
7x(9x + 3) = 7x(9/x + 8/7)
63x^2 + 21x = 63 + 8x
63x^2 + 13x − 63 = 0.
Discriminant: Δ = 13^2 − 4·63·(−63) = 169 + 15876 = 16045 > 0, so there are two distinct real roots for x (neither is 0). Each gives a y, so the system has 2 solutions.
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