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Oksi-84 [34.3K]
2 years ago
12

What is the solution of the linear-quadratic system of equations? y=x^2+5x−3 y−x=2

Mathematics
2 answers:
vovangra [49]2 years ago
5 0

y = x²+5x−3

y−x = 2     =    y = x+2

----------------------------------

x+2 = x²+5x-3

x² + 4x -5 =0

(x+5)(x-1)=0

x ₁= -5

x₂ = 1

-----------------------------------

y₁ = -5+2

y₁ = -3

y₂ = 1+2

y₂ = 3

Vsevolod [243]2 years ago
4 0

Answer:

x =  1, y = 3

x = -5, y = -3

Step-by-step explanation:

Point Form:

(1,3) , (-5, -3)

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Subtract. Write the difference in simplest form.<br><br>(5n - 3) - (-2n + 7)​
kolezko [41]

Answer:

Simplifying

(5n + -3) + -1(-2n + 7) = 0

Reorder the terms:

(-3 + 5n) + -1(-2n + 7) = 0

Remove parenthesis around (-3 + 5n)

-3 + 5n + -1(-2n + 7) = 0

Reorder the terms:

-3 + 5n + -1(7 + -2n) = 0

-3 + 5n + (7 * -1 + -2n * -1) = 0

-3 + 5n + (-7 + 2n) = 0

Reorder the terms:

-3 + -7 + 5n + 2n = 0

Combine like terms: -3 + -7 = -10

-10 + 5n + 2n = 0

Combine like terms: 5n + 2n = 7n

-10 + 7n = 0

Solving

-10 + 7n = 0

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '10' to each side of the equation.

-10 + 10 + 7n = 0 + 10

Combine like terms: -10 + 10 = 0

0 + 7n = 0 + 10

7n = 0 + 10

Combine like terms: 0 + 10 = 10

7n = 10

Divide each side by '7'.

n = 1.428571429

Simplifying

n = 1.428571429

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What are the exact solutions of x^2 − 3x − 7 = 0?
bulgar [2K]

<u>Given</u>:

The given equation is x^{2} -3x-7=0

We need to determine the exact solutions of the equation.

<u>Exact solution:</u>

The exact solution of the equation can be determined by solving the equation using quadratic formula,

x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

From the equation the values are a = 1, b = -3 and c = -7

Thus, substituting these values in the equation, we get;

x=\frac{-(-3) \pm \sqrt{3^2-4(1)(-7)}}{2(1)}

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