Question

what are the values of x and y for the following system of linear equation? 2x-y=2 and x+3y=15 (a) 4 and 5 (b) 5and 4 (c) 3 and 4 (d) 4and 4


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Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The values of x and y for the following system of linear equation 2x - y = 2 and x + 3y = 15

(a) 4 and 5

(b) 5 and 4

(c) 3 and 4

(d) 4 and 4

EVALUATION

Here the given system of equations are

2x - y = 2 - - - - - - (1)

x + 3y = 15 - - - - - - (2)

From Equation 1 we get

y = 2x - 2 - - - - - - (3)

From Equation 2 we get

$\displaystyle \sf{ x + 3(2x - 2) = 15}$

$\displaystyle \sf{ \implies x + 6x - 6 = 15}$

$\displaystyle \sf{ \implies 7x = 15 + 6}$

$\displaystyle \sf{ \implies 7x = 21}$

$\displaystyle \sf{ \implies x = \frac{21}{7} }$

$\displaystyle \sf{ \implies x = 3 }$

From Equation 3 we get

$\displaystyle \sf{ y = (2 \times 3) - 2}$

$\displaystyle \sf{ \implies y = 6 - 2}$

$\displaystyle \sf{ \implies y = 4}$

Hence the required solution is x = 3 , y = 4

FINAL ANSWER

Hence the correct option is (c) 3 and 4

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