Question

$\frac{x}{2} + y = 0.8 \\ \\ \frac{7}{x + \frac{y}{2} } = 10$
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Answer 1

Answer:

• x = 0.4
• y = 0.6

Step-by-step explanation:

 $\sf \dfrac{x}{2}+y=0.8 \\\\ \dfrac{x+2y}{2}=0.8 \\\\ x+2y =0.8 \times 2 \\\\ x+2y=1.6 \ -[1]$

$\sf \dfrac{7}{x+ \dfrac{y}{2}}=10 \\\\ 7=10(x + \dfrac{y}{2}) \\\\ x+\dfrac{y}{2}=\dfrac{7}{10} \\\\ x+\dfrac{y}{2}=0.7 \\\\ \dfrac{2x+y}{2}=0.7 \\\\ 2x+y=0.7 \times 2 \\\\ 2x+y=1.4 \ -[2]$

Multiply equation [1] by 2,

2(x + 2y) = 2(1.6)

2x + 4y = 3.2 - [3]

Subtract equation [2] from [1],

2x + 4y - (2x + y) = 3.2 - 1.4

2x + 4y - 2x - y = 1.8

  3y = 1.8

   y = 1.8/3

   y = 0.6

Substitute y = 0.6 in equation [1],

x + 2y = 1.6

x + 2(0.6) = 1.6

x + 1.2 = 1.6

x = 1.6 - 1.2

x = 0.4

Verification :

 $\sf \dfrac{0.4}{2}+0.6=0.8 \\\\ 0.2 + 0.6 = 0.8 \\\\ 0.8 =0.8 \\\\ LHS=RHS$

 

$\sf \dfrac{7}{0.4+ \dfrac{0.6}{2}}=10 \\\\ \dfrac{7}{0.4+0.3}=10 \\\\ \dfrac{7}{0.7}=10 \\\\ \dfrac{70}{7}=10 \\\\ 10=10 \\\\ LHS=RHS$

Hence verified!