The three system of equations are 9a + 3b + c = 8, 75a + 15b + 3c = 20, and 36a + 6b + c = 5.
<h3>What is a solution to a system of equations? (SOLUTION GRAPHICALLY)</h3>
For a solution to be the solution to a system, it must satisfy all the equations of that system, and like all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at a single point(as we need a common point, which is going to be the intersection of course)(this can be one or many, or sometimes none).
The general equation of parabola is given as,
y = ax² + bx + c
The first point is (3,8), therefore, we can write,
8 = a(3)² + b(3) + c
9a + 3b + c = 8
The second point is (5, 20/3), therefore, we can write,
20/3 = a(5)² + b(5) + c
75a + 15b + 3c = 20
The third point is (6, 5), therefore, we can write,
5 = a(6)² + b(6) + c
36a + 6b + c = 5
Hence, the three system of equations are 9a + 3b + c = 8, 75a + 15b + 3c = 20, and 36a + 6b + c = 5.
Learn more about System of equations:
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