What is the solution to the following system of equations?
y = -x² - 5x - 4, y = -x² + 9x - 18

Solution: Given a set of linear equations

y = -x² - 5x - 4 --- (1)

y = -x² + 9x - 18 --- (2)

Solve linear equations by equating (1) and (2) and isolate the variable x.

-x² - 5x - 4 = -x² + 9x - 18

⇒ -x² - 5x - 4 + x² - 9x + 18] =0

⇒ -x² - 5x - 4 + x² - 9x + 18 = 0

⇒ -14x + 14 = 0

⇒ 14x = 14

⇒ x = 1

 Put the value of x in eq(1) for finding the value of y

⇒ y = -12 - 5.1 - 4

⇒ y = -1 - 5 - 4

⇒ y = -10

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What is the solution to the following system of equations?
y = -x² - 5x - 4, y = -x² + 9x - 18

Summary:

The solution to the set of equations y = -x² - 5x - 4, y = -x² + 9x - 18 is x = 1 and y = -10.