Question

2/x+5/y=1 60/x+40/y=19

Answer 1

Solve the following systems of equations:

2/x +5/y = 1

60/x +40/y =19,

Answer 2

Values are $\bf x = 4$ and $\bf y = 10$.

Given:

• $\frac{2}{x} + \frac{5}{y} = 1\quad...eq1$ and
• $\frac{60}{x} + \frac{40}{y} = 19\quad...eq2$

To find:

• Find the value of x and y.

Solution:

Step 1:

Let

$\bf \frac{1}{x} = a \quad...eq3$

and

$\bf \frac{1}{y} = b \quad...eq4$

Put the values form eq 3 and eq4 in eq1 and eq2.

So,

$\bf \red{2a + 5b = 1}\quad...eq5$

and

$\bf \red{60a + 40b = 19}\quad...eq6$

Step 2:

Solve eqs 5 and 6 for a and b.

Multiply eq5 by 30 and subtract both equations 5 and 6.

$60a + 150b = 30 \\ 60a + 40b = 19 \\ ( - ) \: \: ( - ) \: \: ( - ) \\ - - - - - - - - \\ 110b = 11 \\ - - - - - - - -$

$\implies b = \frac{11}{110}$

$\implies \bf b = \frac{1}{10}$

Put the value of b in eq 6

$60a + 40 \times \frac{1}{10} = 19$

$60a + 4 = 19$

$60a = 15$

$\implies a = \frac{15}{60}$

$\implies \bf a = \frac{1}{4}$

Step 3:

Find the value of x and y.

Put the values of a and b in eqs 3 and 4 to find the value of x and y respectively.

As,

$\frac{1}{x} = \frac{1}{4}$

so,

$\bf \green{x = 4}$

and

$\frac{1}{y} = \frac{1}{10}$

$\bf \green{y = 10}$

Thus,

Values are $\bf x = 4$ and $\bf y = 10$.

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