Question

solve the system of linear equation by substitution method. x-2y+3 and 2x+3y=8​

Answer 1

Answer:

$\rm \bullet \:\: x = 7$

$\rm \bullet \:\: y = 2$

Explanation:

Given equations,

$\rm \bullet \: \: x - 2y = -3 \bf . . . . (i)$

$\rm \bullet \: \: 2x + 3y = 8\bf. . . . . . (ii)$

Taking eq. (i) :-

$\rm \implies \: x - 2y = - 3$

$\rm \implies \: x = - 3 + 2y$

Substituting ‘x’ in eq.(ii) :-

$\rm \implies \: 2x + 3y = 8$

$\rm \implies \: 2(-3 + 2y) + 3y = 8$

$\rm \implies \: -6 + 4y + 3y = 8$

$\rm \implies \: 7y = 8 + 6$

$\rm \implies \: 7y = 14$

$\rm \implies \: y = \dfrac{14}{7}$

$\rm \implies \: y = 2$

Again, substituting ‘y’ in eq.(i) :-

$\rm \implies \: x - 2y = 3$

$\rm \implies \: x - 2(2) = 3$

$\rm \implies \: x - 4 = 3$

$\rm \implies \: x = 3 + 4$

$\rm \implies \: x = 7$

$\rm \therefore \: x = 7$

∴ Required answer:

$\rm \bullet \:\: x = 7$

$\rm \bullet \:\: y = 2$

Answer 2

Question :-

solve the system of linear equation by substitution method. x-2y+3 and 2x+3y=8.

Solution :-

Given Equation :-

➦ x - 2y + 3 --------------(1)

➦ 2x + 3y = 8 -----------(2)

By equation (1)

➨ x - 2y + 3 = 0

➨ x - 2y = -3

➨ x = -3 + 2y

Substitute x = - 3 + 2y in equation (2)

➨ 2(-3 + 2y) + 3y = 8

➨ -6 + 4y + 3y = 8

➨ 7y = 14

➨ y = 14/7

➨ y = 2

Now, put y = 2 in equation (1)

➨x - 2(2) + 3 = 0

➨ x - 4 + 3 = 0

➨ x - 1 = 0

➨ x = 1

Final answer :

➢ x = 1

➢ y = 2

Verification :-

Substituting x = 1 and y = 2 in equation (1)

➨ x - 2y + 3 = 0

➨ 1 - 2(2) + 3 = 0

➨ 1 - 4 + 3 = 0

➨ 1 - 1 = 0

➨ 0 = 0

Hence Verified !

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