Question

Please answer this by using elimination method:

x - 3y = 3x – 1= 2x – y.
If u answer this correctly I'll mark u as brainliest!​

Answer 1

Step-by-step explanation:

$\Longrightarrow x - 3y = 3x - 1 = 2x - y$

LET CONSIDER TWO EQUATIONS TOGETHER AT A SAME TIME AND LETS EQUATE THEM TO GET THE VALUE OF 2 UNKNOWN VARIABLES

$\Longrightarrow \: x - 3y = 3x - 1 \\ \Longrightarrow \: x - 3x - 3y = - 1 \\ \Longrightarrow \: - 2x - 3y = - 1 \\ \Longrightarrow \: - 1(2x + 3y) = - 1 \\ \Longrightarrow2x + 3y = 1 - - - - - - (1st \: equation)$

Now considering another two EQUATIONS TOGETHER.

$\star\underline{\underline{\bold{we \: get :}}}$

$\Longrightarrow \: 3x - 1 = 2x - y \\ \Longrightarrow \: x + y = 1 - - - - - - (2nd \: equation).$

NOW EQUATING BOTH THE EQUATIONS TOGETHER:-

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*multiply 2nd EQUATION with 2 both the side:-

$\Longrightarrow2(x + y) = 2 \\ \Longrightarrow2x + 2y = 2 - - - - - - (2nd \: equation).$

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NOW EQUATING BOTH EQUATIONS TOGETHER WE GET:--

SUBSTRACTING EQUATION 1 WITH EQUATION 2.

$\Longrightarrow \: equation(1) - equation(2).$

$\Longrightarrow2x + 3y - 2x - 2y = 1 - 2 \\\Longrightarrow \: y = - 1$

$\Longrightarrow \: 2x + 2y = 2 \\ \Longrightarrow \: x = \frac{2 - 2y}{2} \\ \Longrightarrow \: x = \frac{2 - 2( - 1)}{2} \\ \Longrightarrow \: x = \frac{2 + 2}{2} \\ \Longrightarrow \: x = 2$

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- STAY BRAINLY

Answer 2

ANSWER

Given,

x - 3y = 3x - 1 = 2x - y

$\red\downarrow \small{ \sf{write \: in \: system}} \\ \red\downarrow \: \: \: \small\sf{ of \: equations} \\ \\ \begin{cases} { \rm{x - 3y = 2x - y}} \\ { \rm{3x - 1 = 2x - y}} \end{cases}$

Taking similar terms on one side

$\begin{cases} { \rm{x - 2x = 3y - y}} \\ { \rm{x + y = 1}} \end{cases} \\ \\ \begin{cases} { \rm{x = - 2y }} \\ { \rm{x + y = 1}}\end{cases}$

Substituting value of x in the other equation

We get

→ x + y = 1

→ - 2y + y = 1

→ - y = 1

→ y = -1

Substitute the value of y into the equation

→ x + y = 1

→ x = 1 + 1

→ x = 2

VERIFICATION:

Substituting x = 2 & y = - 1

x - 3y = 3x - 1 = 2x - y

♦ 2 - 3(-1) = 3(2) - 1 = 2(2) - (-1)

♦ 2 + 3 = 6 - 1 = 4 + 1

♦ 5 = 5 = 5

Are all equal

Hence, verified

Hence, x = 2 & y = - 1