Question

if x+y=26 and 4x+2y=98 then value of x and y?​ please explain.​

Answer 1

Given :

• x + y = 26 [Equation 1]
• 4x + 2y = 98 [Equation 2]

Aim :

• To find x and y respectively

Solution :

By using substitution method, let us find the values of x and y.

Substitution method :

When two Linear equation in two variables is given, we find the value of one variable from the first equation and substitute that value in the second equation.

Equation 1 :

→ x + y = 26

Transposing x to the other side,

→ y = 26 - x

Equation 2 :

Let us substitute the value of y as 26 - x.

→ 4x + 2y = 98

→ 4x + 2(26 - x) = 98

→ 4x + 52 - 2x = 98

→ 2x + 52 = 98

Transposing 52 to the other side,

→ 2x = 98 - 52

→ 2x = 46

Transposing 2 to the other side,

$\implies \sf x = \dfrac{46}{2}$

Reducing to the lowest terms,

$\implies \sf x = 23$

Hence, x = 23

Let us substitute the value of x as 23 in the equation 1 to find the value of y.

→ x + y = 26

→ 23 + y = 26

→ y = 3

Therefore x takes a value of 23 and y takes a value of 3 in the equations.

Elimination method :

In this method, one variable is eliminated so The final equation when the two equations are added or subtracted, formed is a Linear equation in one variable.

• x + y = 26 [Equation 1]
• 4x + 2y = 98 [Equation 2]

Let us eliminate the variable y.

LCM of coefficients of y in both equations = 2.

Hence, multiplying Equation 1 with 2,

→ 2(x + y = 26)

→ 2x + 2y = 52

Subtracting Equation 1 from Equation 2,

→ (4x + 2y = 98) - (2x + 2y = 52)

$\implies 4x + 2y = 98 \\ - 2x - 2y = - 52$

→ 2x = 46

Hence, x = 23 and y = 3.

Answer 2

Answer:

Given :

x + y = 26 [Equation 1]

4x + 2y = 98 [Equation 2]

Aim :

To find x and y respectively

Solution :

By using substitution method, let us find the values of x and y.

Substitution method :

When two Linear equation in two variables is given, we find the value of one variable from the first equation and substitute that value in the second equation.

Equation 1 :

→ x + y = 26

Transposing x to the other side,

→ y = 26 - x

Equation 2 :

Let us substitute the value of y as 26 - x.

→ 4x + 2y = 98

→ 4x + 2(26 - x) = 98

→ 4x + 52 - 2x = 98

→ 2x + 52 = 98

Transposing 52 to the other side,

→ 2x = 98 - 52

→ 2x = 46

Transposing 2 to the other side,

\implies \sf x = \dfrac{46}{2} ⟹x=

2

46

Reducing to the lowest terms,

\implies \sf x = 23⟹x=23

Hence, x = 23

Let us substitute the value of x as 23 in the equation 1 to find the value of y.

→ x + y = 26

→ 23 + y = 26

→ y = 3

Therefore x takes a value of 23 and y takes a value of 3 in the equations.

Elimination method :

In this method, one variable is eliminated so The final equation when the two equations are added or subtracted, formed is a Linear equation in one variable.

x + y = 26 [Equation 1]

4x + 2y = 98 [Equation 2]

Let us eliminate the variable y.

LCM of coefficients of y in both equations = 2.

Hence, multiplying Equation 1 with 2,

→ 2(x + y = 26)

→ 2x + 2y = 52

Subtracting Equation 1 from Equation 2,

→ (4x + 2y = 98) - (2x + 2y = 52)

\begin{gathered} \implies 4x + 2y = 98 \\ - 2x - 2y = - 52\end{gathered}

⟹4x+2y=98

−2x−2y=−52

→ 2x = 46

Hence, x = 23 and y = 3.