Question

3x+2y=25
3x-2y=11
by substitute method
​

Answer 1

Step-by-step explanation:

6x= 36

x = 6

3×6 +2y=25

2y = 25 -18

y = 7/2

y= 3.5

Answer 2

★ How to do :-

Here, we are given with two equations. We are asked to find the value of x and y using substitution method. By using the first equation we will find the value of x by substituting the values. Then, we use the hint of x and then we can find the value of y. Then we can find the original value of x by using the value of y. Here, we also shift numbers from one hand side to the other which changes it's sign. So, let's solve!!

$\:$

➤ Solution :-

${\sf \leadsto 3x + 2y = 25 \: - - - (i)}$

${\sf \leadsto 3x - 2y = 11 \: - - - (ii)}$

By taking equation number one,

${\sf \leadsto 3x + 2y = 25}$

Shift the value 2y from LHS to RHS, changing it's sign.

${\sf \leadsto 3x = 25 - 2y}$

Shift the value 3 from LHS to RHS, changing it's sign.

${\sf \leadsto x = \dfrac{25 - 2y}{3} \: - - - (iii)}$

By substituting equation (iii) in equation (ii),

${\sf \leadsto 3 \bigg( \dfrac{25 - 2y}{3} \bigg) - 2y = 11}$

Cancel the number 3 in denominator and the whole number on LHS.

${\sf \leadsto \not{3} \bigg( \dfrac{25 - 2y}{\not{3}} \bigg) - 2y = 11}$

${\sf \leadsto 25 - 2y - 2y = 11}$

Add the values having same variables.

${\sf \leadsto 25 - 4y = 11}$

Shift the number 25 from LHS to RHS, changing it's sign.

${\sf \leadsto - 4y = 11 - 25}$

Subtract the values on RHS.

${\sf \leadsto - 4y = - 14}$

Shift the value - 4 from LHS to RHS, changing it's sign.

${\sf \leadsto y = \dfrac{-14}{-4}}$

Remove subtraction sign on both sides of fraction.

${\sf \leadsto y = \dfrac{14}{4}}$

$\:$

Value of x :-

By equation (iii),

${\sf \leadsto \dfrac{25 - 2y}{3}}$

Substitute the value of y.

${\sf \leadsto \dfrac{25 - 2 \bigg( \dfrac{14}{4} \bigg)}{3}}$

Cancel the fraction on the numerator.

${\sf \leadsto \dfrac{25 - 2 \bigg( \dfrac{7}{2} \bigg)}{3}}$

Cancel the common number 2 on the numerator.

${\sf \leadsto \dfrac{25 - 7}{3}}$

Simplify the fraction.

${\sf \leadsto x = \dfrac{18}{3} = 6}$

$\:$

So,

Value of x :- ${\sf 6}$

Value of y :- ${\sf \dfrac{7}{2}}$ (when simplified)