The set of equations that can be considered are (i) y = x + 13 and second one is (ii) y = x² + 3x + 10
A set of equations that can all be solved collectively is known as a system of equations.
The general form of the quadratic equation can be represented as y = a.x² + b.x + c, where a, b, and c are real number.
Consequently, the equation system that can be constructed is as follows:
(1) y = x + 13
(2) y = x² + 3x + 10
Method for solving;
x² + 3x + 3 = x + 13
x² + 3x - x +10 -13 = 0
x² + 2x - 3 = 0
x (x + 3) - 1 (x+ 3) = 0
x = -3 or 1
if x = -3, y = 10
if x = 1 then, y = 14
Hence, the system of equation that includes one linear equation is y = x + 13, and the system of equation that includes quadratic equation is y = x² + 3x + 10.
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