Math, asked by amritjha68, 10 months ago

solve the following pair of linear equations by the substitution and cross-multiplication method: 8x+2y=9
3x+2y=4.

don't spam i will report your answer.

Answers

Answered by reachmeatsuraj21

Answer:

Step-by-step explanation:

8x+2y=9

3x+2y=4

4(8x+2y)= 9(3x+2y)

32x+8y=27x+18y

32x-27x=18y-8y

5x=10y

x=2y

substituting on 1,

16y+2y=9

18y=9

y=1/2

therefore,

x=2y

2*1/2

x=1

x=1 and y=1/2

hope this helps you brother...........

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge{\fcolorbox{red}{#ffdfff}{x = 1}}$ and $\huge{\fcolorbox{red}{#ffdfff}{y = 1/2}}$

$\LARGE{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

Two equations :

8x + 2y = 9 ——————————( 1 )
3x + 2y = 4 ——————————( 2 )

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

x and y by the following methods :

Substitution method
Cross-multiplication method

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$

Linear Equations in Two Variables

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

$\large\boxed{1}$ : $\large\boxed{Substitution \: \: method}$

We have,

$\large{8x + 2y = 9}$

$\large{ \implies 2y = 9 - 8x}$

$\large{ \implies y = \frac{9 - 8x}{2} }$ ——————————(3)

On substituting $\large{ y = \frac{9 - 8x}{2} }$ in (2), we get :

$\large{ \longmapsto 3x + 2 \left( \frac{9 - 8x}{2} \right) = 4}$

$\large{ \implies 3x + \cancel{2} \left( \frac{9 - 8x}{ \cancel{2} } \right) = 4}$

$\large{ \implies 3x + 9 - 8x = 4}$

$\large{ \implies (3 - 8)x + 9 = 4}$

$\large{ \implies - 5x = 4 - 9}$

$\large{ \implies - 5x = - 5}$

$\large{ \implies \cancel{ - 5} x = \cancel{ - 5} }$

$\large{ \implies x = 1}$

On substituting x = 1 in (3), we get :

$\large{ y = \frac{9 - 8(1)}{2} }$

$\large{ \implies y = \frac{9 - 8}{2} }$

$\large{ \implies y = \frac{1}{2} }$

Thus, we got :

x = 1
y = 1/2

$\large\boxed{2}$ : $\large\boxed{Cross-multiplication \: \: method}$

The equations are of the form :

$a_1x + b_1y + c_1 = 0$
$a_2x + b_2y + c_2 = 0$

By cross multiplication,

$\LARGE{ x = \frac{ \: b_1c_2 \: + \: b_2c_1 \: }{ \: a_1b_2 \: + \: a_2b_1 \: } }$

AND

$\LARGE{ y = \frac{ \: c_1a_2 \: + \: c_2a_1 \: }{ \: a_1b_2 \: + \: a_2b_1 \: } }$

You can find x and y by this formula.... then you will get x = 1 and y = 1/2.....for sure.

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

${\fcolorbox{green}{#82ffff}{\textcolor{#300061}{your required answer is above ......... keep smiling ….. :)}}}$ $<marquee direction="down" scrollamount="1/10">❤just love❤</marquee>$ $<marquee direction="up" scrollamount="1/10">❤just love❤</marquee>$

$\bold{hope.... \: it \: helps.}$

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$\huge{\fcolorbox{red}{orange}{brainliest \: answer}}$

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solve the following pair of linear equations by the substitution and cross-multiplication method: 8x+2y=9 3x+2y=4.don't spam i will report your answer.​

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Two equations :

Linear Equations in Two Variables

solve the following pair of linear equations by the substitution and cross-multiplication method: 8x+2y=9
3x+2y=4.

don't spam i will report your answer.