Question

$3x - 2y = 0 \\ 5x + y = 13$
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Answer 1

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Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{\mathfrak{\: Given , \: }} \\ \\ \: \: \: \: \: \tt{3x - 2y = 0 \: \: - - - - - - > (1)} \\ \\ \: \: \tt{5x + y = 13\: \: - - - - - - > (2)}$

$\sf{(2) \implies \: y = 13 - 5x \: \: - - - - - - > (3)}$

$\underline{ \text{ \: \: Putting the value of \: \red{y} \: from eq. (3) in eq. (1), we get, \: \: }}$

$\tt{(1) \implies \: 3x - 2y = 0}\\ \\ \: \: \: \: \: \: \: \tt{\implies \: 3x - 2 \red{( 13 - 5x)} = 0} \\ \\ \: \: \: \: \: \: \: \tt{ \implies \: 3x - 26 + 10x = 0 } \\ \\ \: \: \: \: \: \: \: \tt{ \implies \: 13x - 26 = 0} \\ \\ \: \: \: \: \: \: \: \tt{ \implies \: 13x = 26} \\ \\ \: \: \: \: \: \: \: \tt{ \implies \: x = \frac{26}{13} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ \therefore \: \: \red{ x = 2}}$

$\underline{ \text{ \: \: Putting the value of \: \red{x} \: in eq. (3), we get, \: \: }}$

$\sf{ (3) \implies \: y = 13 - 5x} \\ \\ \: \: \: \: \: \: \: \sf{ \implies \: y = 13 - 5 \times \red{2}} \\ \\ \: \: \: \: \: \: \: \sf{ \implies \: y = 13 - 10} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\sf{ \therefore \: \red{y = 3}}$

$\huge{ \bold{ \therefore \: \underline{ \red{x = 2} }\: \: \: and \: \: \: \underline{\red{ y = 3 }}}}$