Question

5x-3y=11 and 2x-y=5 find x and y​

Answer 1

Answer:

The values of x and y are x = 4 & y = 3.

Step-by-step-explanation:

The given linear equations are

5x - 3y = 11 - - - ( 1 ) &

2x - y = 5 - - - ( 2 )

⇒ y = 2x - 5

By substituting this value in equation ( 1 ), we get,

5x - 3y = 11 - - - ( 1 )

⇒ 5x - 3 * ( 2x - 5 ) = 11

⇒ 5x - 6x + 15 = 11

⇒ - x = 11 - 15

⇒ - x = - 4

⇒ x = 4

By using this value,

y = 2x - 5

⇒ y = 2 * 4 - 5

⇒ y = 8 - 5

⇒ y = 3

∴ The values of x and y are x = 4 & y = 3.

Answer 2

STEP-BY-STEP EXPLANATION:

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$\bf We \: have,$

$\tt 5x - 3y = 11 \: \: \: ...(1) \\ \tt 2x - y = 5 \: \: \: \: \: \: \: \: ...(2)$

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$\bf By \: Elimination \: Method,$

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$\tt Multiply \: \: Eq [2] \: \: by \: \: 3 \: \: to \: \: make \: \: \: \\ \tt the \: \: coefficients \: \: of \: \: y \: \: equal,$

$\tt 6x - 3y = 15 \: \: \: ...(3)$

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$\tt Substract \: \: Eq [1] \: \: from \: \: Eq [3] \: \: to \\ \tt eliminate \: \: y, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$:\implies\tt (6x - 3y) - (5x - 3y) = 15 - 11$

$:\implies\tt 6x - 3y - 5x + 3y = 4$

$:\implies\tt x = 4$

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$\tt Substitute \: \: this \: \: value \: \: of \: \: y \: \: in \: \: Eq[2],$

$\tt 2x - y = 5 \: \: \: ...(2)$

$:\implies\tt 2(4) - y = 5$

$:\implies\tt 8 - y = 5$

$:\implies\tt y = 8 - 5$

$:\implies\tt y = 3$

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$\bf{ Hence, \tt x = 4 \: \: and \: \: y = 3}$

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VERIFICATION,

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$\tt 5x - 3y = 11 \: \: \: ...(1)$

$:\implies\tt 5(4) - 3(3) = 11$

$:\implies\tt 20 - 9 = 11$

$:\implies\tt 11 = 11$

$:\implies\tt LHS = RHS$

.

$:\implies\tt 2x - y = 5 \: \: \: ...(2)$

$:\implies\tt 2(4) - 3 = 5$

$:\implies\tt 8 - 3 = 5$

$:\implies\tt 5 = 5$

$:\implies\tt LHS = RHS$

.

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REQUIRED ANSWER,

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• $\tt x = 4 \: \: and \: \: y = 3$