Question

Find x and y if 6x + 10y = 10 and 14x + 3y = 14.
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Answer 1

Answer:

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Answer 2

If 6x + 10y = 10 and 14x + 3y = 14 then, ​$x = \frac{55}{61}\ and\ y = \frac{28}{61}$

Solution:

Given system of equations are:

6x + 10y = 10 -------- eqn 1

14x + 3y = 14 --------- eqn 2

Multiply eqn 1 by 3

18x + 30y = 30 ------ eqn 3

Multiply eqn 2 by 10

140x + 30y = 140 -------- eqn 4

Subtract eqn 3 from eqn 4

140x + 30y = 140

18x + 30y = 30

( - ) ------------------

122x = 110

$x = \frac{110}{122} \\\\x = \frac{55}{61}$

$Substitute\ x = \frac{55}{61}\ in\ eqn\ 1$

$6 \times \frac{55}{61} + 10y = 10\\\\ \frac{330}{61} + 10y = 10\\\\ 10y = 10 - \frac{330}{61} \\\\ 10y = \frac{280}{61}\\\\ y = \frac{28}{61}$

Thus $x = \frac{55}{61}\ and\ y = \frac{28}{61}$

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