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3 years ago

How many solutions are there to thesystem of equations, x + y = 1and 2x + 2y = 2?

Mathematics

1 answer:

larisa86 [58]3 years ago

6 0

There are infinitely many solutions of the system of equations, x + y = 1

and 2x + 2y = 2

Step-by-step explanation:

We need to find how many solutions are there to the system of equations.

$x+y=1\,\,\,(1)\\2x+2y=2\,\,\,(2)$

Solving:

Multiply equation (1) with 2 and subtract with equation(2)

$2x+2y=2\\2x+2y=2\\-\,\,-\,\,\,\,\,\,\,\,\,\,\,\,-\\------\\0=0$

Since our answer is 0=0 so, there are infinitely many solutions.

Keyword: Systems of equations

Learn more about Systems of equations at:

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Urgent. Please show all work

myrzilka [38]

Answer:

$\displaystyle f'(x) = \frac{4}{x^2}$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Differentiation

Derivatives
Derivative Notation

The definition of a derivative is the slope of the tangent line: $\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle f(x) = -\frac{4}{x}$

Step 2: Differentiate

[Function] Substitute in x: $\displaystyle f(x + h) = -\frac{4}{x + h}$
Substitute in functions [Definition of a Derivative]: $\displaystyle f'(x) = \lim_{h \to 0} \frac{-\frac{4}{x + h} - \big( -\frac{4}{x} \big)}{h}$
Simplify: $\displaystyle f'(x) = \lim_{h \to 0} \frac{4}{x(x+ h)}$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle f'(x) = \frac{4}{x(x+ 0)}$
Simplify: $\displaystyle f'(x) = \frac{4}{x^2}$

∴ the derivative of the given function will be equal to 4 divided by x².

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Learn more about derivatives: brainly.com/question/25804880

Learn more about calculus: brainly.com/question/23558817

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

Unit: Differentiation

6 0

2 years ago

Find the midpoint of AC is at -2 and C is at 3 on a number line

Bad White [126]

2c3 Because when you look at it when you look at the question if I do that and then you were at the AC is at the two and see is that the three on the number line then you would add that on and you’ll get your answer

3 0

3 years ago

A bill originally amounting Rs 1550, now amounts to Rs 1736 after adding VAT. Find the VAT rate.kaabil original amounting

Vlad [161]

Answer: 12%

Step-by-step explanation:

Original amount = Rs 1550

VAT = Rs 1736 - Rs 1550 = Rs 186

VAT rate = VAT/Original amount × 100

= 186/1550 × 100

= 18600/1550

= 12%

Therefore, the VAT rate is 12%.

Check:

= Rs 1550 + (12% × Rs 1550)

= Rs 1550 + $186

= Rs 1736

4 0

3 years ago

the area of nathans bedroom rug is 15 square feet the longer side measures 5 feet his living room rug is twice as long as wide a

Slav-nsk [51]

What is your question?

6 0

3 years ago

The sum of four consecutive integers is 134. Find the integers. (please show your work)

lidiya [134]

Answer:

Integers: 32,33,34,35

Step-by-step explanation:

Consecutive means back-to-back, with a difference of 1

Therefore this can be represented with the following equation (where x is the first number), and we can set this equal to the sum

$x+(x+1)+(x+2)+(x+3)=134\\4x+6=134\\4x=128\\x=32$

Therefore since x = 32, all four integers are:

$32,33,34,35$

If we check this, we can see that their sum equals to 134

$32+33+34+35 = 134$

Hope this helps!

8 0

3 years ago

How many solutions are there to thesystem of equations, x + y = 1and 2x + 2y = 2?​

How many solutions are there to thesystem of equations, x + y = 1and 2x + 2y = 2?