Question

Solve the following pair of linear equations using substitution method :-

2x+3y + 5 = 0 ; 5x-3y+9=0​

Answer 1

Answer:

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

It is easier to eliminate y by just adding both equations. For eliminating x, we will have to multiply equation (i) by 5 and equation (ii) by 2 and then subtract equation (ii) from (i).

So, Add both equations
=> (5+2)x +(3-3)y + (5+9) = 0
=> 7x + 14 = 0
=> x = -14 / 7
=> x = -2

To calculate y, substitute x in eq (i)
=> 2x(-2) + 3y + 5 = 0
=> -4 + 3y = -5
=> 3y = -5+4
=> y = -1/3

Therefore,
x = -2, y = -1/3