Question

solve 5x+y=20, 10x-2y=50 by substitution method pleas Koi solve kr do important ​

Answer 1

Basic Concept Used :-

To solve systems using substitution, follow this procedure:

• Select one equation and solve it to get one variable in terms of second variables.

• In the second equation, substitute the value of variable evaluated in Step 1 to reduce the equation to one variable.

• Solve the new equation to get the value of one variable.

• Substitute the value found in to any one of two equations involving both variables and solve for the other variable.

Let's solve the problem now!!

↝ Given Linear Equations are

$\rm :\longmapsto\:5x + y = 20 - - - (1)$

and

$\rm :\longmapsto\:10x - 2y = 50 - - - (2)$

↝ From equation (1), we have

$\rm :\longmapsto\:y \: = \: 20 - 5x - - - (3)$

↝ Substituting the value of y in equation (2),

$\rm :\longmapsto\:10x - 2(20 - 5x) = 50$

$\rm :\longmapsto\:10x - 40 + 10x = 50$

$\rm :\longmapsto\:20x = 50 + 40$

$\rm :\longmapsto\:20x = 90$

$\bf\implies \:x = \dfrac{9}{2} - - - (4)$

↝ On substituting the value of x in equation (3), we get

$\rm :\longmapsto\:y = 20 - 5 \times \dfrac{9}{2}$

$\rm :\longmapsto\:y = 20 - \dfrac{45}{2}$

$\rm :\longmapsto\:y = \dfrac{40 - 45}{2}$

$\bf\implies \:y \: = \: - \: \dfrac{5}{2}$

$\overbrace{ \underline { \boxed { \bf \therefore The \: solution\: is \: x \: = \: \dfrac{9}{2} \: \: and \: \:y \: = - \: \dfrac{5}{2}}}}$

Additional Information

There are 4 methods to solve this type of pair of linear equations.

• 1. Method of Substitution

• 2. Method of Eliminations

• 3. Method of Cross Multiplication

• 4. Graphical Method

Answer 2

Answer:

x = 9/2 and y = -5/2

Step-by-step explanation:

The given equations are :

5x + y = 20       ...(1)

10x - 2y = 50    ...(2)

From equation (1), we get;

5x + y = 20

5x = 20 -y

x = (20 - y)/5

Substituting x = (20 - y)/5 in equation (2), we get;

10 (20 - y)/5 - 2y = 50

(200 - 10y)/5 -2y = 50

(200 - 10y -10y)/5 = 50

200 - 20y = 50 x 5

200 - 20y = 250

-20y = 250 - 200

-20y = 50

y = 50/-20

y = -5/2

Substituting the value of y in equation (1), we get;

5x + y = 20

5x + (-5/2) = 20

5x - 5/2 = 20

(10x - 5)/2 = 20

10x - 5 = 20 x 2

10x - 5 = 40

10x = 40 + 5

10x = 45

x = 45/10

x = 9/2

Hope it helps u...