Question

Solve the following pair of linear equations by both elimination and substitution method 1) 3x+4y=10; 2x+2y=2​

Answer 1

$\huge{\underline{Solution}}$

※ By elimination method:

$⟹\sf{3x + 4y = 10}$ .... (i)

$⟹\sf{2x – 2y = 2}$ ... (ii)

※ Multiplying equation (ii) by 2, we get

$⟹\sf{4x – 4y = 4}$ ... (iii)

$⟹\sf{3x + 4y = 10}$ ... (i)

※ Adding equation (i) and (iii), we get

$⟹\sf{7x + 0 = 14}$

※ Dividing both side by 7, we get

$⟹\sf{x = \dfrac{14}{7}}$

$⟹\sf{x = 2x=2}$

※ Putting in equation (i), we get

$⟹\sf{3x + 4y = 10}$

$⟹\sf{3(2) + 4y = 10}$

$⟹\sf{6 + 4y = 10}$

$⟹\sf{4y = 10 – 6}$

$⟹\sf{4y=4}$

$⟹\sf{y = \dfrac{4}{4}}$

$⟹\sf{y=1}$

Hence, answer is x = 2, y = 1

※ By substitution method:

$⟹\sf{3x + 4y = 10}$....(i)

※ Subtract 3x both side, we get

$⟹\sf{4y = 10 – 3x}$

※ Divide by 4 we get

$\sf{y = \dfrac{10 - 3x}{4}}$

※ Putting this value in equation (ii), we get

$⟹\sf{2x – 2y = 2}$...(i)

$⟹\sf{2x - 2 \dfrac{(10 - 3x )}{4}}$

※ Multiply by 4 we get

$⟹\sf{8x - 2(10 – 3x) = 8}$

$⟹\sf{8x - 20 + 6x = 8}$

$⟹\sf{14x = 28}$

$⟹\sf{x = \dfrac{28}{14} = 2}$

$⟹\sf{y = \dfrac{(10 - 3x)}{4}}$

$⟹\sf{y = \dfrac{4}{4}}$

$⟹\sf{y=1}$

Hence, answer is x = 2, y = 1 again.