In the given problem, apply your knowledge in algebra and basic mathematics specially in solving word problem about solving unknown variables, and equation of line, circle and others.
In order to have intersection, the value of x and y are the same for both equation of line and circle.
y = 3x + 10
x² + y² = 10
x² + (3x + 10)² = 10
x² + 9x² + 60x + 100 = 10
10x² + 60x + 90 = 0
x² + 6x + 9 = 0
(x + 3)(x + 3) = 0
x = -3
x = - 3
y = 3x + 10
y = 3(-3) + 10
y = -9 + 10
y = 1
Therefore, they will intersect at point (-3,1).
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