Question

Solve × + y = 14 and × - y = 4 by elimination method

Answer 1

Given:

• x + y = 14 → → → [Equation 1]

• x - y = 4. → → →. [Equation 2]

To find:

➟ Value of x and y.

Method:

Adding the 2 Equations,

x + y = 14

{+} x - y = 4

2x = 14 + 4

⇒2x = 18

⇒x = 18 ÷ 2

⇒ x = 9

Now, Substitute value of x in any one of the Equations to find out the value of y

Here we have Substituted in Equation 2

x - y = 4

⇒9 - y = 4

⇒y = 5

Verification:

Substitute value of x and y in the given Equations to verify

x + y = 14

⇒9 + 5 = 14

⇒14 = 14

LHS = RHS

x - y = 4

⇒9 - 5 = 4

⇒4 = 4

LHS = RHS

Hence verified

Additional information:

1. For solving linear pair of Equations in 2 variables, we can solve it by either Elimination method or Substitution method.
2. Elimination method includes either addition of Equations or subtraction of equations.

Answer 2

Answer:

$\boxed{\bold{\large{Answer :}}}$

$\bold{x = 9}$

$\bold{y = 5}$

Step-by-step explanation:

$\boxed{\bold{\large{Question \: :}}}$

Solve x + y = 14 and x - y = 4 by elimination method.

$\boxed{\bold{\large{Given \: :}}}$

✏ x + y = 14⠀‎‏‏⠀⠀⠀— — (1)

✏ x - y = 4 ⠀‎‏‏ ⠀⠀⠀— — (2)

$\boxed{\bold{\large{Solution :}}}$

Adding Equation (1) and Equation (2). We get ,

⇒ (x + y) + (x - y) = 14 + 4

⇒ x + y + x - y = 18

⇒ 2x = 18

⇒ x = 18/2

⇒ x = 9

Now putting the value of x in Equation (1). We get ,

⇒ x + y = 14

⇒ 9 + y = 14

⇒ y = 14 - 9

⇒ y = 5

$\boxed{\bold{\large{Answer :}}}$

$\bold{x = 9}$

$\bold{y = 5}$

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$\boxed{\bold{\mapsto \: Confused\: \: \: let's \: \: \: \: verify \: \: :)}}$

$\bold{x = 9}$

$\bold{y = 5}$

Putting the values of x and y in Equation (1). We get ,

✏ x + y = 14

x + y

= 9 + 5

= 14

$\bold{x \: + y = 14}$

$\bold{Verified \: !}$

✏ x - y = 4 ⠀‎‏‏ ⠀⠀— — (2)

9 - 4

= 5

$\bold{x \: - y = 4}$

$\bold{Verified \: !}$

Now we are confirmed that our answer is correct.

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❤️ Happy Studying ! ☺️