Question

What is the solution to the following system of equations?

y = −x2 − 5x − 4
y = −x2 + 9x − 18

(−1, −10)
(1, −10)
(−1, 10)
(1, 10)

Answer 1

choice 2 is correct.

Explanation:

We have given the following system of equations

y = x² - 5x -4 ( eq I )

y = -x² + 9x - 18 ( eq II)

Putting the value of y from (eq I) in (eq II).

-x²-5x-4 = -x²+ 9x - 18

-x²+x²-5x-9x-4+18 = 0

-14x +14 =0

-14x = -14

x = -14 / -14

x= 1

Putting the value of x in equation I to find the value of y

y = -(1)² - 5(1) -4

y = -1 -5-4

So,(1 ,-10 ) is the solution of given system of equations.

Answer 2

Option 2 ( 1,-10)

Explanation:

The two equations are y = -x²-5x-4 -----(1)

and y = -x²+9x-18-------(2)

To get the solution of these lines we will substitute the value of y form equation 1 to 2.

- x² - 5x -4 = -x²+9x-18

Now by collecting similar terms on each side.

-x² -5x + x²-9x = -18 + 4

-14x = -14

14x = 14

x = 1

By putting the value of x in equation 1.

y = -1 - 5 - 4 = -10

So the solution is (1, -10)

Therefore Option 2 is the correct answer.