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Kamila [148]
4 years ago
15

What are the solutions to the system of equations?

Mathematics
1 answer:
svet-max [94.6K]4 years ago
6 0

Answer:the third option is correct

Step-by-step explanation:

The system of equations are

y = 2x^2 - 5x - 7 - - - - - - - - - - -1

y = 2x + 2 - - - - - - - - - - - - - 2

We would equate equation 1 and equation 2. It becomes

2x^2 - 5x - 7 = 2x + 2

2x^2 - 5x - 2x - 7 - 2 = 0

2x^2 - 7x - 9 = 0

We would find two numbers such that their sum or difference is -7x and their product is - 18x^2. The two numbers are 2x and - 9x. Therefore

2x^2 + 2x - 9x - 9 = 0

2x(x + 1) - 9(x + 1) = 0

2x - 9 = 0 or x + 1 = 0

2x = 9 or x = - 1

x = 9/2 = 4.5

Substituting x = 4.5 or x = -1 into equation 2, it becomes

y = 2 × 4.5 + 2 or y = 2 × - 1 + 2

y = 11 or y = 0

Therefore, the solutions are

(4.5, 11) (- 1, 0)

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Solve the quadratic equation by taking the square root of (x+5)^2=16
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(x-5)2=16


The first step you can take to solve this quadratic is to take the square root of both sides of the equation.

√[(x-5)2]=√(16)

When you take the square root of a term that is square it equals what is inside the parentheses.

So on the left side, you have x-5

On the right side, you are what we call "forcing" the square root. When this happens, you need to put ±. Why? Good question. When you square a negative number it positive; when you square a positive number it is also positive.

The √16 = ±4

So now we have;
x-5=±4

What do you do with that?
You make two separate equations.

x-5=4 and x-5=-4
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Let's check our answers

x=9

(x-5)2=16
(9-5)2=16
42=16
16=16 it checks

x=1

(x-5)2=16
(1-5)2=16
(-4)2=16
16=16 it also checks


ANSWER: x=9 and x=1
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