Question

please answer fast step
by step
solve the equation 2x-3y=6 and x+y=1 (3mark)
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Answer 1

SolutioN :

We have, Pair of Linear Equation.

2x - 3y = 6.

x + y = 1.

Taking Equation ( 2 )

→ x + y = 1.

→ y = 1 - x.__________ ( 3 )

Now, Putting the value of y in Equation ( 1 )

→ 2x - 3y = 6.

→ 2x -3( 1 - x ) = 6.

→ 2x - 3 + 3x = 6.

→ 5x = 6 + 3.

→ 5x = 9.

→ x = 9 / 5.

Now, Putting the value of x = 9 / 5.

→ y = 1 - x.

→ y = 1 - 9 / 5.

→ y = 5 - 9 / 5.

→ y = - 4 / 5.

Therefore, the value of x is 9 / 5 and y = - 4 / 5.

$\rule{200}3$

VerificatioN :

Taking Equation ( 1 )

→ 2x - 3y = 6.

→ 2( 9 / 5 ) - 3( - 4 / 5 ) = 6.

→ 18 / 5 + 12 / 5 = 6.

→ 30 / 5 = 6.

→ 6 = 6.

Taking Equation ( 2 )

→ x + y = 1.

→ 9 / 5 - 4 / 5 = 1.

→ 9 - 4 / 5 = 1.

→ 5 / 5 = 1.

→ 1 = 1.

Hence Verify.

Answer 2

$\large\underline\purple{\bold{Solution :- }}$

$\sf{\underbrace{\underline{ \rm \: According\ to\ the\ question:-}}}$

$: \implies \: \tt \: 2x - 3y = 6 - - - (1) \\ : \implies \: \tt \: x + y = 1 \: \: \: \: - - - (2)$

☆ On multiply equation (2) by 3, we get

$: \implies \: \tt \: 2x - 3y = 6 \: \: \: \: - - - (1) \\ : \implies \: \tt \: 3x + 3y = 3 \: \: \: \: - - - (3)$

☆ On adding equation (1) and (3), we get

$: \implies \: \tt \: 5x = 9 \\ : \implies \: \tt \boxed {\red {\tt \: \: x \: = \: \dfrac{9}{5}}}$

☆ On substituting the value of 'x', we get

$: \implies \: \tt \: \dfrac{9}{5} + y = 1 \\ : \implies \: \tt \: y \: = 1 - \dfrac{9}{5} \\ : \implies \: \tt \: y \: = \dfrac{5 - 9}{5}$

$: \implies \: \tt \boxed {\red {\tt \: \: y \: = \: - \: \dfrac{4}{5}}}$

$\begin{gathered}\begin{gathered}\bf So - \begin{cases} &\rm{ \red{x = \dfrac{9}{5}} } \\ \\ &\rm{ \purple{y = - \: \dfrac{4}{5} }} \end{cases}\end{gathered}\end{gathered}$