Question

Solve:2x-3y=19 and 3x-2y=21 by substitution method

Answer 1

Answer : The equations given to us are:

2x−3y=19 ...(1)

3x−2y=21 ...(2)

By substitution method, we will substitute the value of y from equation 1 in equation 2.

∴ from first equation y=

3

(2x−19)

So by substituting the value of y in the second equation,

The second equation becomes:

3x−

3

2(2x−19)

=21

⇒

3

9x−4x+38

=21

⇒5x=63−38

⇒5x=25

⇒x=5

Substituting the value of x in equation number (1) we get ,

2(5)−3y=19

⇒10−19=3y

⇒−9=3y

⇒y=−3

then y from above equation will be −3.

Answer 2

Answer:

=> The value of x is 5 and y is -3.

Step-by-step explanation:

Given equations:-

$2x-3y=19$    $...(i)$

$3x-2y=21$    $...(ii)$

By substitution method,

Now, by substituting the value of y from equation ( 1 ) in equation ( 2 ),

From the first equation, $y=\frac{2x-19}{3}=21$

Put the value of y in the ( 2 ) equation,

$=> 3x-\frac{2(2x-19)}{3}=21$

By further simplifying, we get

$=>\frac{9x-4x+38}{3}=21$

$=> 5x=63-38$

$=> 5x=25$

$=> x =5$

So, the value of x is $5.$

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

=> $2(5)-3y=19$

=> $10-3y=19$

=> $10-19=3y$

=> 9 = 3y

=> y = 3

So, the value of y is $3.$