Question

x+y=9 2x+2y=13 using substitution method​

Answer 1

Step-by-step explanation:

Hey mate

x+y = 9 > Eq. 1

2x+2y = 13 > Eq. 2

In eq 1,

x+y = 9

x = 9 - y.

Substituting the value of x in Eq 2,

2x+2y = 13

2( 9 - y ) - 2y = 13

18 - 2y - 2y = 13

-4y = - 5

So, y = 5/4. > Eq. 3

In eq 1,

x + y = 9

x + 5/4 = 9

4x + 5 = 36

x = 31/4

I hope it helps you

Answer 2

Given:-

$x + y = 9$ (P)

$2x + 2y = 13$ (Q)

From equation P,

$x = 9 - y$

Putting the value of $x$ in Q:-

$2(9 - y) + 2y = 13$

⇒ $18 - 2y + 2y = 13$

⇒ $18 = 13$.

But this is a false statement.

Therefore, the pair has no solutions or is an inconsistent pair.

IMPORTANT:-

Whenever we reach at such circumstances, we may get a:-

• true statement,
• false statement (just as the earlier one).

In case of the true statement, the pair has infinite number of solutions.

But in case of a false statement, there are no solutions.

How can I prove that the pair is inconsistent?

To do so, we know inconsistent pairs are parallel or the ratio of coefficients and constants =

$\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} ≠ \dfrac{c_1}{c_2}$.

You can also see it for the given pair in question. It satisfies the ratio.