Question

find whether the following pairs of linear equations is consistent or not x+y=14,x-y=4 if consistent,what are the solutions ​

Answer 1

Answer:

Step-by-step explanation:

Equation 1 : x + y = 14

Equation 2 : x - y = 4

Here,

• a₁ = 1
• a₂ = 1
• b₁ = 1
• b₂ = -1
• c₁ = 14
• c₂ = 4

For the equations to be consistent, it must satisfy the following cases.

Case 1:

If a₁ / a₂ ≠ b₁ / b₂ then the following are consistent.

In this case, 1 / 1 ≠  1 / -1

Hence this case works.

Since it works, the solutions are consistent.

Finding Solutions:

Adding both the equations, we get,

⇒ x + y + x - y = 14 + 4

⇒ 2x + 0y = 18

⇒ 2x = 18

⇒ x = 18/2 = 9

Substituting the value of x in any of the equations we get,

⇒ x + y = 14

⇒ 9 + y = 14

⇒ y = 14 - 9

⇒ y = 5

Hence the values of x and y are 9 and 5 respectively.

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Answer 2

$\frac{ x_{1}}{x_{2}}not \: equal \: to \: \frac{ y_{1}}{y_{2}}$
Therefore consistent.
Solution in the attachment.
$x = 9 \: and \: y = 5$