1.

2x+3y = 12,5x-3y=9 ans plz​

Answer»

GIVEN:-

EQUATION:-

2x + 3y = 12

5x - 3y = 9

To find:-

The VALUE of x and y

Method Used:-

Substitution method.

Solution:-

\sf{2x + 3y = 12\longrightarrow[i]}

\sf{5x - 3y = 9\longrightarrow}

From equation[i]

\sf{2x + 3y = 12}

= \sf{2x = 12-3y}

= \sf{x = \dfrac{12-3y}{2}}

SUBSTITUTING the value of x in equation[ii]

= \sf{5x - 3y = 9}

= \sf{5\bigg(\dfrac{12-3y}{2}\bigg) - 3y = 9}

= \sf{\dfrac{60-15y}{2} - 3y = 9}

= \sf{\dfrac{60-15y-6y}{2} = 9}

= \sf{60-21y = 9\times2}

= \sf{-21y = 18-60}

= \sf{-21y = -42}

= \sf{y = \dfrac{-42}{-21}}

= \sf{y = 2}

Now,

Putting the value of y in equation[i]

\sf{2x + 3y = 12}

= \sf{2x + 3\times 2 = 12}

= \sf{2x + 6 = 12}

= \sf{2x = 12-6}

= \sf{2x = 6}

= \sf{x = \dfrac{6}{2}}

= \sf{x = 3}

\sf{\therefore x = 3\: and\: y = 2}

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Verification:-

Let us put the value of x and y in both the equations simultaneously.

For equation[i]

= \sf{2x + 3y = 12}

= \sf{2\times3 + 3\times 2 = 12}

= \sf{6 + 6 = 12}

= \sf{12 = 12} [Verified]

For equation[ii]

= \sf{5x - 3y = 9}

= \sf{5\times 3 - 3\times 2 = 9}

= \sf{15 - 6 = 9}

= \sf{9 = 9} [Verified]

Hence Verified!!!!

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