Question

x/3 - y/3 = 0, 5x + y = 36 plz show how to do​

Answer 1

Answer:

x = 6

y = 6

Step-by-step explanation:

Check the image

Answer 2

Answer:

Algebraic methods of solving simultaneous linear equations in two variables.

★ The most commonly used algebraic methods of solving simultaneous linear equations in two variables are :

$\bullet \: \:$ Method of Elimination by substitution.

$\bullet \: \:$ Method of Elimination by equating the coefficient.

$\bullet \: \:$ Method of cross - multiplication.

${\boxed{\boxed{\sf{\blue{1. \: Method \: of \: Elimination \: by \: equating \: the \: coefficient.}}}}}$

In this method , we eliminate one of the two variables to obtain an equation in one variable which can easily be solved. By putting the value of this variable in any one of the given equations, the value of the other variable wil comes out.

$\bigstar \: \large{\sf{\purple{Algorithm ( Steps )}}}$

$\bullet \: \:$ Step 1 - Obtain the two equations.

$\bullet \: \:$ Step 2 - Multiply the equations so as to make the coefficients of the variables to be eliminated equal.

$\bullet \: \:$ Step 3 - Add or subtract the equations obtained in step 2 according as the terms having the same coefficients are of opposite or of the same sign.

$\bullet \: \:$ Step 4 - Solve the equation in one variable obtained in step 3.

$\bullet \: \:$ Step 5 - Substitute the value found in step 4 in any one of the given equations and find the value of the other variable.

Answer with steps :

We can solve the following equation :

$\dashrightarrow\:\:\sf \dfrac{x}{3} - \dfrac{y}{3} = 0$

Solving it further by taking L.C.M

$\dashrightarrow\:\:\sf \dfrac{x - y}{3} = 0$

Transposing ' 3 ' to the R.H.S side

$\dashrightarrow\:\:\sf x - y = 0 \times 3$

$\dashrightarrow\:\:\sf x - y = 0$

Considering it Equation (1)

And

$\dashrightarrow\:\:\sf 5x + y = 36$ --- Equation (2)

Now,

We have two equations ,

From equation (1) and (2)

By using Elimination Method :-

$\dashrightarrow\:\:\sf x - y = 0$

$\dashrightarrow\:\:\sf 5x + y = 36$ ( By Addition )

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$\dashrightarrow\:\:\sf 6x = 36$

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$\dashrightarrow\:\:\sf x = \dfrac{36}{6}$

$\dashrightarrow\:\:\bf x = 6$

Hence,

$\dashrightarrow\:\: \underline{ \boxed{\sf The \: value \: of \: x = {\red 6}}}$

Now, Putting (x = 6) in equation (1) to find out the value of y.

$\dashrightarrow\:\:\sf 6 - y = 0$

$\dashrightarrow\:\:\sf - y = - 6$

$\dashrightarrow\:\:\bf y = 6$

$\dashrightarrow\:\: \underline{ \boxed{\sf The \: value \: of \: y = {\red 6}}}$

What we have done ?

Here, we used the method of elimination by equating coefficient. As the coefficient was already equal so we simply eliminated the y from the equation and got the value of x and thereafter we substituted the value of x in the other equation to get the value of y. That's how we got the values of x and y respectively.

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Checking the answer :-

Verification :

Putting (x = 6) and (y = 6) respectively in Equation (2)

$\dashrightarrow\:\:\sf 5x + y = 36$

$\dashrightarrow\:\:\sf 5(6) + 6 = 36$

$\dashrightarrow\:\:\sf 30 + 6 = 36$

$\dashrightarrow\:\:\bf 36 = 36$

$\dashrightarrow\:\:\sf L.H.S = R.H.S$

Hence,

${\boxed {\sf{Verified ! }}}$

${\bf {\purple{Other \: Method :}}}$

${\boxed{\boxed{\sf{\blue{Method \: of \: Elimination \: by \: substitution}}}}}$

In this method, we express one of the variables in terms of the other variable from either of the two equations and then this expression is put in the other equation to obtain an equation in one variable.

$\bigstar \: \large{\sf{\red{Algorithm ( Steps )}}}$

$\bullet \: \:$ Step - 1 Obtain the two equations.

Consider the equations be :

$\implies \sf a_1x + b_1y + c_1 = 0$ --- (1)

and,

$\implies \sf a_2x + b_2y + c_2 = 0$ --- (2)

$\bullet \: \:$ Step - 2 Choose either of the two equations, let us we take equation (1) and find the value of one variable, say y , in terms of the other i.e, x.

$\bullet \: \:$ Step - 3 Substitute the value of y, obtained in Step 2 , in the other equation i.e, (2) to get an equation in x.

$\bullet \: \:$ Step - 4 Solve the equation obtained in step 3 to get the value of x.

$\bullet \: \:$ Step 5 Substitute the value of x obtained in step 4 in the expression for y in terms of x obtained in step 2 to get the value of y.

$\bullet \: \:$ Step 6 The values of x and y obtained in steps 4 and 5 respectively.

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