Question

solve the following equations by using the methods of substitution. 2x+3y=9 3x+4y=5​

Answer 1

Step-by-step explanation:

We have,

2x+3y=9 ……. (1)

3x+4y=5 …… (2)

Now,

y=

3

9−2x

On putting the value of y, in equation (2), we get

3x+4(

3

9−2x

)=5

3x+

3

36−8x

=5

9x+36−8x=15

x=15−36

Now, put the value of x in equation (1), we get

y=

3

9−2(−21)

y=

3

9+42

y=

3

51

=17

Hence, this is the answer.

Answer 2

Answer

$\sf \dashrightarrow 2x + 3y = 9 \: \: --- (i)$

$\sf \dashrightarrow 3x + 4y = 5 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 2x + 3y = 9$

$\sf \dashrightarrow 2x = 9 - 3y$

$\sf \dashrightarrow x = \dfrac{9 - 3y}{2}$

Now, let's find the value of y by second equation.

$\sf \dashrightarrow 3x + 4y = 5$

$\sf \dashrightarrow 3 \bigg( \dfrac{9 - 3y}{2} \bigg) + 4y = 5$

$\sf \dashrightarrow \dfrac{27 - 9y}{2} + 4y = 5$

$\sf \dashrightarrow \dfrac{27 - 9y + 8y}{2} = 5$

$\sf \dashrightarrow \dfrac{27 - 1y}{2} = 5$

$\sf \dashrightarrow 27 - 1y = 5 \times 2$

$\sf \dashrightarrow 27 - 1y = 10$

$\sf \dashrightarrow -1y = 10 - 27$

$\sf \dashrightarrow -1y = -17$

$\sf \dashrightarrow y = \dfrac{-17}{-1}$

$\sf \dashrightarrow y = 17$

Now, let's find the value of x by first equation.

$\sf \dashrightarrow 2x + 3y = 9$

$\sf \dashrightarrow 2x + 3(17) = 9$

$\sf \dashrightarrow 2x + 51 = 9$

$\sf \dashrightarrow 2x = 9 - 51$

$\sf \dashrightarrow 2x = -42$

$\sf \dashrightarrow x = \dfrac{-42}{2}$

$\sf \dashrightarrow x = -21$

Hence, the values of x and y are -21 and 17 respectively.