Question

solve the following pairs of linear equations by the substitution method

x + y =14
x - y =4​

Answer 1

Answer:

x+y=14-equation 1

1x-y=4-equation 2

adding equation 1 and 2 we get,

adding equation 1 and 2 we get, x+y=14

adding equation 1 and 2 we get, x+y=14x-y=4

adding equation 1 and 2 we get, x+y=14x-y=42x=18

adding equation 1 and 2 we get, x+y=14x-y=42x=18x=18/2

adding equation 1 and 2 we get, x+y=14x-y=42x=18x=18/2x=9

put x=9 in equation 2

put x=9 in equation 2x-y=4

put x=9 in equation 2x-y=49-y=4

put x=9 in equation 2x-y=49-y=49-4=y

put x=9 in equation 2x-y=49-y=49-4=yy=5

put x=9 in equation 2x-y=49-y=49-4=yy=5 therefore x=9 and y=5

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Answer 2

Given equations:

• x + y = 14 and x - y = 4

★ Using Substituting Method:

• The method of solving "by substitution" works by solving one of the equations for one of the variables, and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other.

Let x + y = 14 eq [1]

And, x - y = 4 eq [2]

Now, from eq [1]

⇒ x + y = 14

⇒ x = 14 - y eq [3]

Now, Putting value eq [3] in eq [2],

⇒ (14 - y) - y = 4

⇒ 14 - y - y = 4

⇒ 14 - 2y = 4

⇒ - 2y = 4 - 14

⇒ - 2y = - 10

⇒ y = 10/2

⇒ y = 5

Now, Putting value of y in eq [3]

⇒ x = 14 - 5

⇒ x = 9

Hence, Solved!