Question

Solve by the method of substitution : 4/X + 9/y = 1/2 and 12/ x + 12/ y = 1 : x.y not= 0​

Answer 1

Answer:

x=20 and y =30

Step-by-step explanation:

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Answer 2

Answer:

The values of x and y in the given equation by substitution method is x=20 and y=30 for  $x\neq 0$ and $y\neq 0$

Step-by-step explanation:

Given equations are $\frac{4}{x}+\frac{9}{y}=\frac{1}{2}\hfill (1)$

and $\frac{12}{x}+\frac{12}{y}=1\hfill (2)$  for $x\neq 0$ and $y\neq 0$

Now solving the given equations by substitution method :

Let $a=\frac{1}{x}$ and $b=\frac{1}{y}$ for $x\neq 0$ and $y\neq 0$

Equation (1) implies $4a+9b=\frac{1}{2}\hfill (3)$

Equation (2) implies $12a+12b=1\hfill (4)$

From equation (3) $4a+9b=\frac{1}{2}$

$4a=\frac{1}{2}-9b$

$a=\frac{\frac{1}{2}-9b}{4}$

$a=\frac{1}{8}-\frac{9b}{4}$

• Now substitute the value of "a" in equation (4)

$12(\frac{1}{8}-\frac{9b}{4})+12b=1$

$\frac{12}{8}-\frac{108b}{4}+12b=1$

$\frac{3}{2}-27b+12b=1$

$-15b=1-\frac{3}{2}$

$-15b=\frac{2-3}{2}$

$-15b=-\frac{1}{2}$

$b=\frac{1}{2\times 15}$

$b=\frac{1}{30}$

Since $b=\frac{1}{y}$  for  $y\neq 0$

$b=\frac{1}{30}=\frac{1}{y}$ for  $y\neq 0$

Therefore y=30

• Substitute the value of b in equation $a=\frac{1}{8}-\frac{9b}{4}$ we get

$a=\frac{1}{8}-\frac{9(\frac{1}{30})}{4}$

$=\frac{1}{8}-\frac{\frac{9}{30}}{4}$

$=\frac{1}{8}-\frac{9}{120}$

$=\frac{1}{8}-\frac{3}{40}$

$=\frac{5-3}{40}$

$=\frac{2}{40}$

$a=\frac{1}{20}$

Since $a=\frac{1}{x}$ for $x\neq 0$

$a=\frac{1}{20}=\frac{1}{x}$ for $x\neq 0$

Therefore x=20

Therefore x=20 and y=30