Solve the following systems of equations using elimination method.
$\frac{3 x}{2} - \frac{5 y}{3} = - 2, \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

(2, 3)

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(3, 3)

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(2, 4)

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None of these

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Solution

The correct option is A $(2, 3)$
Consider the given equations.
$\frac{3 x}{2} - \frac{5 y}{3} = - 2$

$9 x - 10 y = - 12$ $- - - - - - - (1)$

$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

$2 x + 3 y = 13$ $- - - - - - - (2)$

On multiplying by $2$ in equation $(1)$ and multiplying by $9$ in equation $(2)$ and subtract, we get

$18 x - 20 y = - 24$
$18 x + 27 y = 117$
—————————
$- 47 y = 141$
$y = 3$ $[$ put in $(2)]$

$2 x + 3 \times 3 = 13$

$2 x + 9 = 13$

$2 x = 4$

$x = 2$

Hence, the value of $x$ is $2$ and the value of $y$ is $3$ .

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Similar questions

\frac{5}{x} - \frac{4}{y} = - 2, \frac{2}{x} + \frac{3}{y} = 13

Solve the following system of equations using elimination method:
$2 x + 7 y = 10$
$3 x + y = 6$

Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution:

$\frac{3 x}{2} - \frac{5 y}{3} + 2 = 0$

$\frac{x}{3} + \frac{y}{2} = 2 \frac{1}{6}$

\frac{3 x}{2} - \frac{5 y}{3} = - 2, \frac{x}{3} + \frac{y}{2} = \frac{13}{6}

x + \frac{y}{2} = 4, \frac{x}{3} + 2 y = 5

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