Required solution :
Here we have been given with two equations,
From the first equation,
⇒ 2x - y = 13
⇒ -y = 13 - 2x
⇒ y = 2x - 13
Here we got a temporary value of y as 2x - 13 .
In second equation,
Substitute here the value of y as 2x - 13 inorder to get the value of x.
⇒ 3x + (2x - 13) = 12
⇒ 3x + 2x - 13 = 12
⇒ 5x - 13 = 12
⇒ 5x = 12 + 13
⇒ 5x = 25
⇒ x = 25 / 5
⇒ x = 5
★ Therefore, value of x is 5.
Finding out value of y :
Substitute the value of x in this equation.
⇒ y = 2x - 13
⇒ y = 2 (5) - 13
⇒ y = 2 × 5 - 13
⇒ y = 10 - 13
⇒ y = -3
★ Therefore, value of y is -3.
Topic : Linear equations in two variables.
Given :
Solution :
Now,
(i) + (ii)
[tex]\qquad \sf \: { \dashrightarrow 2x - y +(3x + y) = 13 + 12}[/tex]
[tex]\qquad \sf \: { \dashrightarrow 2x \: \cancel{- \: y} +3x \: \cancel{+ \: y}= 25}[/tex]
[tex]\qquad \sf \: { \dashrightarrow 2x \: +3x= 25}[/tex]
[tex]\qquad \sf \: { \dashrightarrow 5x= 25}[/tex]
[tex]\qquad \sf \: { \dashrightarrow x \: = \dfrac{25}{5} }[/tex]
[tex]\qquad {\pmb{ \bf { \dashrightarrow x \: = 5 }}}[/tex]
Now, substituting the value of x in Eq (ii) :
[tex]\qquad \sf \: { \dashrightarrow 3x + y = 12}[/tex]
[tex]\qquad \sf \: { \dashrightarrow 3(5) + y = 12}[/tex]
[tex]\qquad \sf \: { \dashrightarrow 15 + y = 12}[/tex]
[tex]\qquad \sf \: { \dashrightarrow y = 12 - 15}[/tex]
[tex]\qquad \pmb {\bf { \dashrightarrow y = - 3}}[/tex]
Therefore, The value of x = 5 and y = -3 .
