if 3x/2-y/3=2 and x/2+y/3=13/6 so what …
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Sia ? 6 years, 6 months ago
The given system of equations may be written as
{tex}9x -10y + 12 = 0{/tex} ...(i)
{tex}2x + 3y - 13 = 0{/tex}.... (ii)
From (ii), we get {tex} y = \frac { 13 - 2 x } { 3 }{/tex}
Substituting {tex} y = \frac { 13 - 2 x } { 3 }{/tex} in (i), we get
{tex} 9 x - \frac { 10 ( 13 - 2 x ) } { 3 } + 12 = 0{/tex}
{tex} \Rightarrow{/tex} {tex}27x - 10(13 - 2x) + 36 = 0{/tex}
{tex} \Rightarrow{/tex} {tex}27x -130 + 20x + 36 = 0{/tex}
{tex} \Rightarrow{/tex} {tex}47x - 94 = 0{/tex}
{tex} \Rightarrow{/tex} {tex}47x = 94{/tex}
{tex} \Rightarrow x = \frac { 94 } { 47 } = 2{/tex}
Substituting {tex}x = 2{/tex} in (i), we get
9 {tex} \times{/tex} 2 - 10y + 12 = 0
{tex} \Rightarrow 10 y = 30 {/tex}
{tex}\Rightarrow y = \frac { 30 } { 10 } = 3{/tex}
Hence, x = 2 and y = 3 is the required solution.
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