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3 years ago

Systems of equations with different slopes and different y-intercepts have more than one solution. (5 points)

Mathematics

2 answers:

vaieri [72.5K]3 years ago

8 0

Answer:

The correct answer would be never

Step-by-step explanation:

The systems of linear equations can have:

1. No solution: When the lines have the same slope but different y-intercept. This means that the lines are parallel and never intersect, therefore, the system of equations has no solution.

2. One solution: When the lines have different slopes and intersect at one point in the plane. The point of intersection will be the solution of the system

3. Infinitely many solutions: When the lines have the same slope and the y-intercepts are equal. This means that the equations represents the same line and there are infinite number of solution.

Therefore, based on the explained above, the conclusion is: Systems of equations with different slopes and different y-intercepts never have more than one solution.

I hope this helps

antiseptic1488 [7]3 years ago

3 0

Answer:

The answer should be never, I took the test and I got it right!

Step-by-step explanation:

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4 years ago

Find a formula for dy/dx if sin x + cos y + sec(xy) = 251

Lena [83]

Answer:

$\displaystyle \frac{dy}{dx} = \frac{-cos(x) - ysec(xy)tan(xy)}{-sin(y) + xsec(xy)tan(xy)}$

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Factoring

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Trig Differentiation

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Implicit Differentiation

Step-by-step explanation:

Step 1: Define

Identify

sin(x) + cos(y) + sec(xy) = 251

Step 2: Differentiate

[Implicit Differentiation] Trig Differentiation [Chain Rule]: $\displaystyle cos(x) - sin(y)\frac{dy}{dx} + sec(xy)tan(xy) \cdot (y + x\frac{dy}{dx}) = 0$
[Subtraction Property of Equality] Isolate $\displaystyle \frac{dy}{dx}$ terms: $\displaystyle -sin(y)\frac{dy}{dx} + sec(xy)tan(xy) \cdot (y + x\frac{dy}{dx}) = -cos(x)$
[Distributive Property] Distribute sec(xy)tan(xy): $\displaystyle -sin(y)\frac{dy}{dx} + ysec(xy)tan(xy) + xsec(xy)tan(xy)\frac{dy}{dx} = -cos(x)$
[Subtraction Property of Equality] Isolate $\displaystyle \frac{dy}{dx}$ terms: $\displaystyle -sin(y)\frac{dy}{dx} + xsec(xy)tan(xy)\frac{dy}{dx} = -cos(x) - ysec(xy)tan(xy)$
Factor out $\displaystyle \frac{dy}{dx}$ : $\displaystyle \frac{dy}{dx}[-sin(y) + xsec(xy)tan(xy)] = -cos(x) - ysec(xy)tan(xy)$
[Division Property of Equality] Isolate $\displaystyle \frac{dy}{dx}$ : $\displaystyle \frac{dy}{dx} = \frac{-cos(x) - ysec(xy)tan(xy)}{-sin(y) + xsec(xy)tan(xy)}$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

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