Question

solve by substitution method 0.4x+0.3y=1.7 and 0.7x+0.2y=0.8​

Answer 1

Answer:

• x = 3
• y = 5

Explanation:

Given equations,

$\rm \implies \: 0.4x + 0.3y = 1.7 . . . . . \bf (i)$

$\rm \implies \: 0.7x + 0.2y = 0.8. . . . . . \bf (ii)$

Solving eq.(i) :-

$\rm \implies \: 0.4x + 0.3y = 1.7$

$\rm \implies \: 0.4x = 1.7 - 0.3y$

$\rm \implies \: x = \dfrac{1.7 - 0.3y}{0.4}$

Substituting ‘x’ in eq.(ii) :-

$\rm \implies \: 0.7x + 0.2y = 0.8$

$\rm \implies \: 0.7 \bigg( \dfrac{1.7 - 0.3y}{0.4} \bigg) + 0.2y = 0.$

$\rm \implies \: \dfrac{1.19- 0.21y}{0.4} + 0.2y = 0.8$

$\rm \implies \: \dfrac{1.19- 0.21y + 0.08y}{0.4} = 0.8$

$\rm \implies \: \dfrac{1.19- 0.29y }{0.4} = 0.8$

$\rm \implies \: {1.19- 0.29y }= 0.8\times 0.4$

$\rm \implies \: {1.19- 0.29y }= 0.32$

$\rm \implies \: 1.19- 0.32 = 0.29y$

$\rm \implies \: 0.87= 0.29y$

$\rm \implies \: \dfrac{0.87}{0.29} = y$

$\rm \implies \: \dfrac{87}{29} = y$

$\rm \implies \: 3 = y$

$\rm \therefore \: y = 3$

Substituting ‘y’ in eq.(i) :-

$\rm \implies \: 0.4x + 0.3y = 1.7$

$\rm \implies \: 0.4(3) + 0.3y = 1.7$

$\rm \implies \: 1.2 + 0.3y = 1.7$

$\rm \implies \: 0.3y = 1.7 - 1.2$

$\rm \implies \: 0.3y = 1.5$

$\rm \implies \:y = \dfrac{1.5}{0.3}$

$\rm \implies \:y = \dfrac{15}{3}$

$\rm \implies \:y = 5$

Hence the value of :-

• x = 3
• y = 5

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