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3 years ago

4x+(x-y/8)=17 and 2y+x-(5y+2/4)=2 by using elimination method

Mathematics

1 answer:

vladimir2022 [97]3 years ago

4 0

Answer:

x=811/238, y=36/119. (811/238, 36/119).

Step-by-step explanation:

4x+(x-y/8)=17

2y+x-(5y+2/4)=2

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

4x+x-y/8=17

5x-y/8=17

40x-y=136

y=40x-136

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

2y+x-5y-2/4=2

2y-5y+x-1/2=2

-3y+x=2+1/2

-3y+x=4/2+1/2

-3y+x=5/2

-3(40x-136)+x=5/2

-120x+408+x=5/2

-119x=5/2-408

-119x=5/2-816/2

-119x=-811/2

119x=811/2

x=(811/2)/119

x=(811/2)(1/119)=811/238

y=40(811/238)-136

y=16220/119-136

y=36/119

x=811/238, y=36/119.

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Step-by-step explanation:

We are given the expression:

$\displaystyle \large{(3 - 4i)(6i + 7) - (2 - 3i)}$

First, expand 3-4i in 6i+7. To expand binomial with binomial, first we expand 3 in 6i+7 then expand -4i in 6i+7.

$\displaystyle \large{[(3 \cdot 6i) + (3 \cdot 7) + ( - 4i \cdot 6i) + ( - 4i \cdot 7)]- (2 - 3i)} \\ \displaystyle \large{[18i + 21 - 24 {i}^{2} - 28i]- (2 - 3i)}$

Now combine like terms.

$\displaystyle \large{[ - 10i+ 21 - 24 {i}^{2} ]- (2 - 3i)}$

Imaginary Unit

$\displaystyle \large{i = \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2} = - 1 }$

Therefore:-

$\displaystyle \large{[ - 10i+ 21 - 24 ( - 1) ]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 21 + 24]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 45]- (2 - 3i)}$