# What is the solution of the linear-quadratic system of equation: y = x^{2} + 5x - 3, y - x = 2?

An equation that has a degree equal to two is called a quadratic equation. They have many applications in various fields. Linear equations have a degree equal to one.

## Answer: The solution of the linear-quadratic system of equation: y = x^{2} + 5x - 3, y - x = 2 is (-5, -3) and (1, 3) in the form of (x, y).

Let's understand the solution to the problem.

**Explanation:**

Here, we have two equations:

⇒ y = x^{2} + 5x - 3 ---- (1)

⇒ y - x = 2 ---- (2)

Now, we can write equation (2) as y = x + 2.

Now, we substitute the above value in equation (1).

⇒ (x + 2) = x^{2} + 5x - 3

⇒ x^{2} + 4x - 5 = 0

This is a quadratic equation. Now, we use the quadratic formula to solve the equation above.

⇒ x = (-4 + √(4^{2} - 4(-5))) / 2 = 1

⇒ x = (-4 - √(4^{2} - 4(-5))) / 2 = -5

Therefore, when x = 1, we have y = 3, from eq. 2; and when x = -5, we have y = -3.

### Hence, The solution of the linear-quadratic system of equation: y = x^{2} + 5x - 3, y - x = 2 is (-5, -3) and (1, 3) in the form of (x, y).

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