Math, asked by ashishkasture, 4 months ago

iv) If 3x+2y=10 and 2x+3y=15, find the value of x+y.

Answers

Answered by Anonymous
2

Solution:-

 \rm \to \: 3x + 2y = 10 \:  \:  \:  \:  \:  \: ....(i)eq

 \rm \to \: 2x + 3y = 15 \:  \:  \:  \:  \:  \: ...(ii)eq

Now using substitution method

So Take (i) eq

 \rm \to \: 3x + 2y = 10

 \rm \to \: 3x = 10 - 2y

 \rm \to \: x =  \dfrac{10 - 2y}{3}  \:  \:  \:  \:  \: ...(iii)eq

Now substitute the (iii)eq on (ii)eq

 \rm \to \: 2x + 3y = 15 \:  \:  \:  \:  \:  \: ...(ii)eq

 \rm \to \: 2 \times  \bigg( \dfrac{10 - 2y}{3} \bigg)  + 3y  = 15

 \rm \to \:  \dfrac{20 - 4y}{3}  + 3y = 15

 \rm \to \:  \dfrac{20 - 4y + 9y}{3}  = 15

 \rm \to \: 20 + 5y = 45

 \rm \to \: 5y = 25

 \rm \to \: y = 5

Now put the value of y on (iii)eq

 \rm \to \: x =  \dfrac{10 - 2y}{3}  \:  \:  \:  \:  \:

 \rm \to \: x  = \dfrac{10 - 2 \times 5}{3}

 \rm \to \: x =  \dfrac{0}{3}  =0

So value of x = 0 and y = 5

we have to find x + y

=> 0 + 5 = 5

Answer = 5

Answered by Anonymous
26

\huge\bf\underline\red{Solution}

3x + 2y = 10. _____. eq 1

2x + 3y = 15 ______. eq 2

Myltiply eq 1 with 2

Multiply eq 2 with 3

6x + 4y = 20

6x + 9y = 45. Subtract eq 1 and eq 2

___________

-5y = - 25

y = 5

Sub in eq 1

3x + 10 = 10

3x = 0

x=0

So, x + y = 0+ 5 = 5

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