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2 years ago

Solve the system.

Mathematics

1 answer:

svetoff [14.1K]2 years ago

8 0

Answer:

(0, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

y + 5x = 1

5y - x = 5

Step 2: Rewrite Systems

y + 5x = 1

Subtract 5x on both sides: y = 1 - 5x

Step 3: Redefine Systems

y = 1 - 5x

5y - x = 5

Step 4: Solve for x

Substitution

Substitution in y: 5(1 - 5x) - x = 5
Distribute 5: 5 - 25x - x = 5
Combine like terms: 5 - 26x = 5
Isolate x term: -26x = 0
Isolate x: x = 0

Step 5: Solve for y

Define equation: 5y - x = 5
Substitute in x: 5y - 0 = 5
Subtract: 5y = 5
Isolate y: y = 1

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3 years ago

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Factor completely 4p^2-25q^2

Alexxandr [17]

Answer:

(2p - 5q) (2p + 5q)

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3 years ago

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2 years ago

What is the constant of proportionality of $18.36 for 2 pizzas

sergeinik [125]

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Step-by-step explanation:

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2 years ago

Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)

viktelen [127]

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}$

The first line segment can be parameterized by $\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle$ with $0\le t\le1$ . Denote this first segment by $C_1$ . Then

$\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt$
$=108$

The second line segment ( $C_2$ ) can be described by $\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle$ , again with $0\le t\le1$ . Then

$\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt$
$=-\dfrac{229}3$

Finally,

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3$

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3 years ago