Question

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Solve the following system of linear equations by substitution method:

(1) 2x – y = 2

(2) x + 3y =15​
​

Answer 1

Step-by-step explanation:

2x-y=2 ..........1

x+3y=15..........2

multiple equation 1 with 3

(2x-y)×3=2×3

6x-3y=6

therefore,

6x-3y=6

x+3y=15

-. +. -

____________

x = 9/5

Answer 2

Given :

• Linear equation 2x-y=2 , x+3y=15

To Find :

• Solve the equations by Substitution method .

Solution :

$\longmapsto\tt{2x-y=2----(1)}$

$\longmapsto\tt{x+3y=15----(2)}$

On Solving Equation 1 :

$\longmapsto\tt{2x-y=2}$

$\longmapsto\tt\bf{2x-2=y}$

Subsituting y = 2x-2 in eq. 2 :

$\longmapsto\tt{x+3(2x-2)=15}$

$\longmapsto\tt{x+6x-6=15}$

$\longmapsto\tt{7x-6=15}$

$\longmapsto\tt{7x=15+6}$

$\longmapsto\tt{7x=21}$

$\longmapsto\tt{x=\cancel\dfrac{21}{7}}$

$\longmapsto\tt\bf{x=3}$

Value of x is 3 ...

Now ,

Putting x = 3 in 2x - 2 = y :

$\longmapsto\tt{2(3)-2=y}$

$\longmapsto\tt{6-2=y}$

$\longmapsto\tt\bf{4=y}$

Value of y is 4 ....