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2 years ago

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Solve the following system of equations by substitution. y=-1 5x + 7y = -2

1 answer:

Nady [450]2 years ago

7 0

Answer:

(1,-1)

Step-by-step explanation:

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BabaBlast [244]

$\underline{\bf{Given \:equation:-}}$

$\\ \sf{:}\dashrightarrow ax^2+by+c=0$

$\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.$

$\sf We\:know,$

$\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}$

$\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}$

$\underline{\large{\bf Identities\:used:-}}$

$\boxed{\sf (a+b)^2=a^2+2ab+b^2}$

$\boxed{\sf (√a)^2=a}$

$\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}$

$\boxed{\sf \sqrt{\sqrt{a}}=a}$

$\underline{\bf Final\: Solution:-}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}$

$\bull\sf Apply\: Squares$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}$

$\bull\sf Put\:values$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}$

$\bull\sf Simplify$

$\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}$

$\underline{\bf More\: simplification:-}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}$

$\underline{\Large{\bf Simplified\: Answer:-}}$

$\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}$

5 0

2 years ago

Read 2 more answers

$400 invested at 2% compounded quarterly after a period of 2 years

Anna71 [15]

Final balance = $416.28
total compound interest= $16.28

7 0

3 years ago

180 minus what = 45<br><br> i really need this answer thank you

LuckyWell [14K]

Answer: 135

Step-by-step explanation: All you need to do is 180-45=135.

3 0

3 years ago

Read 2 more answers

which expression represents purely real numbers and which expression represents non-real complex number?

Lyrx [107]

Answer:

Step-by-step explanation:

Complex numbers are the numbers represented by the expression = a + bi

Here a = real part of the number

bi = imaginary part

a and b are the real numbers.

$i^9=(i^2)^4.(i)$

$=(-1)^{4}.i$ [Since, $i^2=-1$ ]

$=i$

Therefore, its a non real complex number.

2 - $\sqrt{-49}$ = $2-\sqrt{(-1)(7)^2}$

= $2-7\sqrt{-1}$

= $2-7i$

This number is a Non real complex number.

$\sqrt{(-18)^2}=18\sqrt{-1}$

= 18i

It's a non real complex number.

3 + 2i

It's a non real complex number.

-289

It's a purely real number.

$4-32i^2=4-32(-1)$

= 4 + 32

= 36

It's a purely real number.

6 0

3 years ago

How do I simplify 5 3/2

Volgvan

Note the improper fraction. Change it into a mixed fraction

3/2 = 2/2 + 1/2

2/2 = 1

5 + 1 1/2

Simplify.

5 + 1 = 6

6 1/2 is your answer

hope this helps

5 0

3 years ago

Read 2 more answers