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

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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

   [tex]\rm :\longmapsto\:5x + y = 20 – – – (1)[/tex]

   and

   [tex]\rm :\longmapsto\:10x – 2y = 50 – – – (2)[/tex]

   ↝ From equation (1), we have

   [tex]\rm :\longmapsto\:y \: = \: 20 – 5x – – – (3)[/tex]

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

   [tex]\rm :\longmapsto\:10x – 2(20 – 5x) = 50[/tex]

   [tex]\rm :\longmapsto\:10x – 40 + 10x = 50[/tex]

   [tex]\rm :\longmapsto\:20x = 50 + 40[/tex]

   [tex]\rm :\longmapsto\:20x = 90[/tex]

   [tex]\bf\implies \:x = \dfrac{9}{2} – – – (4)[/tex]

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

   [tex]\rm :\longmapsto\:y = 20 – 5 \times \dfrac{9}{2} [/tex]

   [tex]\rm :\longmapsto\:y = 20 – \dfrac{45}{2} [/tex]

   [tex]\rm :\longmapsto\:y = \dfrac{40 – 45}{2} [/tex]

   [tex]\bf\implies \:y \: = \: – \: \dfrac{5}{2} [/tex]

   [tex]\overbrace{ \underline { \boxed { \bf \therefore The \: solution\: is \: x \: = \: \dfrac{9}{2} \: \: and \: \:y \: = – \: \dfrac{5}{2}}}}[/tex]

   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

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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…

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