Question

4/x + 5/y = 58 , 7/x + 3/y =67
solve by Cramer's rules? ​

Answer 1

Answer:

4/x + 5/y = 58

7/x + 3/y = 67

4( 1/x ) + 5(1/y) = 58

7(1/x) + 3(1/y) = 67

let's take m and n instead of 1/x & 1/y respectively

4m+5n = 58

7m+3n = 67

D = | 4/7 5/3 |

= 12- 35

= - 23

Dm = | 58/67 5/3 |

= 174 - 335

= - 161

Dn = | 4/7 58/67 |

= 268 - 406

= -138

m = Dm/D

= -161/-23

= 7

n = Dn/D

n = -138/-23

n = 6

m = 1/x = 7 = 1/7

n = 1/y = 6 = 1/ 6

x,y = 1/7,1/6

Answer 2

Value of $x = \frac{1}{7} \: and \: y = \frac{1}{6}$

GIVEN:-

$\frac{4}{x} + \frac{5}{y} = 58 \\ \frac{7}{x} + \frac{3}{y} = 67$

TO FIND:- Solve the given equation by Cramer's rules

SOLUTION:-

• In algebra, Cramer's rule is a formula which is used to solve a system of linear equations that contains as many equations as unknowns, efficient whenever the system of equations has a unique solution.
• Let the constant be D

By evaluating equations

$\frac{4}{x} + \frac{5}{y} = 58 \\ = 4( \frac{1}{x} ) + 5 (\frac{1}{y} )$

$\frac{7}{x} + \frac{3}{y} \\ = 7( \frac{1}{x} ) + 3 (\frac{1}{y} )$

Let $\frac{1}{x} = m$ and $\frac{1}{y} = n$

D = $| \frac{4}{7} \frac{5}{3} | \\ = 12 - 35 \\ = - 23$

Dm = $| \frac{58}{67} \frac{5}{3} | \\ = 174 - 335 \\ = - 161$

Dn = $| \frac{4}{7} \frac{58}{67} | \\ = 268 - 406 \\ = - 138$

m = $\frac{dm}{d} \\ = \frac{ - 161}{ - 23} \\ = 7$

n = $\frac{dn}{n} \\ = \frac{ - 138}{ - 23} \\ = 6$

m= $7 = \frac{1}{x} \\ x = \frac{1}{7}$

n = $6 = \frac{1}{y} \\ y = \frac{1}{6}$

Hence, Value of x = $\frac{1}{7}$

and value of y = $\frac{1}{6}$

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