Question

Solve the following pair of linear equations by substitution and elimination method
3x + 2y = 10 and 2x -2y = 2

Answer 1

$\large{\underline{\bf{\blue{Given:-}}}}$

• ✦ equations:- 3x +2y = 10
• ✦ 2x - 2y = 2

$\large{\underline{\bf{\blue{To\:Find:-}}}}$

✦ value of x and y .

$\huge{\underline{\tt{\purple{Solution:-}}}}$

By substitution method :-

$\\\longmapsto \:$ 3x + 2y = 10.........(i)

$\longmapsto \:$ 2x - 2y = 2.........(ii)

from eq. (i) :-

$\\\longmapsto \:$3x = 10 -2y

$\longmapsto \:$ x =( 10 - 2y)/3.....(iii)

substituting value of x in equation (ii):-

$\\ \longmapsto \:$ 2x - 2y = 2

$\longmapsto \: \sf\: 2 \times ( \frac{10 - 2y}{3} ) - 2y = 2 \\ \\ \longmapsto \: \sf \frac{20 - 4y}{3} = 2 + 2y \\ \\ \longmapsto \: \sf \: 20 - 4y = 6 + 6y \\ \\\longmapsto \: \sf \:20 - 6 = 6y + 4y \\ \\ \longmapsto \: \sf \: 14 = 10y \\ \\ \longmapsto \: \sf \:y = \cancel\frac{14}{10} \\ \\ \longmapsto \: \sf \:y = \frac{7}{5}$

substituting value of y in (ii)

$\longmapsto \rm\:2x - 2y = 2\: \\ \\\longmapsto \rm\:2x - 2( \frac{7}{5} ) = 2 \\ \\ \longmapsto \rm\:2x - \frac{14}{5} = 2 \\ \\ \longmapsto \rm\: \frac{10x - 14}{5} = 2 \\ \\\longmapsto \rm\:10x - 14 = 10 \\ \\ \longmapsto \rm\:10x = 24 \\ \\ \longmapsto \rm\:x = \frac{24}{10} \\ \\ \longmapsto \rm\:x = \frac{12}{5}$

By elimination method:-

$\longmapsto \:$ 3x + 2y = 10.........(i)

$\longmapsto \:$ 2x - 2y = 2.........(ii)

$\rm\:3x + 2y = 10 \\ \rm\:2x - 2y = 2 \\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }\: \\\rm\:5x \: \: \: \: \: \: \: \: \: \: = 12 \\ \\\bf\: \:\: x \: \: \: \: \: \: \: \: \: \: = \frac{12}{ 5}$

putting value of x in equation (ii)

$\longmapsto \rm\:2x - 2y = 2\: \\ \\ \longmapsto \rm\:2 \times \frac{12}{5} = 2 + 2y \\ \\ \longmapsto \rm\: \frac{24}{5} - 2 = 2y \\ \\ \longmapsto \rm\: \frac{24 - 10}{5} = 2y \\ \\ \longmapsto \rm\: \frac{14}{10} = y \\ \\ \longmapsto \bf\: y = \frac{7}{5} \:$

Hence,

• x = 12/5
• y = 7/5

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Answer 2

Solution

Given :-

• Equation, 3x + 2y = 10 ---------Equ(1)
• 2x - 2y = 2 ---------------Equ(2)

Find :-

• Value of x & y by , substitution and elimination method

Explanation

By, Substitution Method

By. euq(1)

==> x = (10-2y)/ 3 ----------------Equ(3)

Keep value of x in equ(2)

==> (10-2y)/3 - y = 1

==> (10-2y)-3y = 3

==> -5y = 3 - 10

==> y = 7/5

Keep Value in equ(1)

==> 3x + 2 * 7/5 = 10

==> 3x = 10 - 14/5

==> 3x = (10*5-14)/5

==> 3x = (50-14)/5

==> 3x = 36/5

==>x = 36/(3*5)

==> x = 12/5

Hence

• Value of x = 12/5
• Value of y = 7/5

__________________

By, Elimination Method

Equation :-

• 3x + 2y = 10 ----------Equ(4)
• 2x - 2y = 2------------Equ(5)

_________________Add it's(Eliminate x)

==> 3x + 2x = 10 +2

==> 5x = 12

==> x = 12/5

Keep value of y in equ(4)

==> 3* 12/5 + 2y = 10

==> 2y = 10 - 36/5

==> 2y = (10*5 - 36)/5

==> 2y = (50-36)/5

==> 2y = 14/5

==> y = 14/(2*5)

==> y = 7/5

Hence

• Value of x = 12/5
• Value of y = 7/5

__________________