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which represents the solution(s) of the system of equations, y=-x2 + 6x + 16 and y = - 4x + 37? determine the solution set
algebraically

The solution set of given algebraic expression is  x = 7 and x = 3

Step-by-step explanation:

Given as :

The polynomial expression are

y = - x² + 6 x + 16                 1

y = - 4 x + 37                        2

Now, Solving these two equation

putting the value of y from eq 2 into eq 1

So, - x² + 6 x + 16 = - 4 x + 37

Or,  - x² + 6 x + 16 + 4 x - 37 = 0

Or, - x² + (6 + 4) x + (16 - 37) = 0

Or, - x² + 10 x - 21 = 0

Now, solving this quadratic equation by middle term break

i.e - x² + 7 x + 3 x - 21 = 0

Or, - x ( x - 7) + 3 ( x - 7) = 0

Or, (x - 7) ( - x + 3) = 0

Or, (x - 7) = 0  and ( - x + 3 ) = 0

∴ x = 7 , x = 3

So, The solution set of given algebraic expression is  x = 7 , x = 3

Hence, The solution set of given algebraic expression is  x = 7 and x = 3 Answer