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# Solve the following system of equations and show all work. y = x^{2} + 3, y = x + 5.

Equations form the basis of mathematics. There are many types of equations, which include quadratic, biquadratic, cubic, linear, and many others.

### Answer: The solution to the given system of equations y = x^{2} + 3, y = x + 5, is x = -1 and x = 2.

Lets' understand the process

**Explanation:**

Given equations:

⇒ y = x^{2} + 3

⇒ y = x + 5

Now, we substitute y = x + 5 in the first equation.

⇒ x + 5 = x^{2} + 3

⇒ x^{2} - x - 2 = 0

Now, we can use the quadratic formula to solve the above equation.

⇒ x = [1 ± √{(-1)^{2} - 4(-2)(1)}] / 2(1)

⇒ x = [1 ± 3] / 2

⇒ x = -1 and x = 2.

### Hence, the solution to the given system of equations is x = -1 and x = 2.

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