Question

check whether 3x+2y=5 ;2x-3y=7 are consistent or inconsistent

Answer 1

$\huge\mathfrak{Answer \ :-}$
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Given equations :-

3x + 2y = 5

And

2x - 3y = 7

Here,

a1 = 3, a2 = 2, b1 = 2, b2 = -3, c1 = 5 and c2 = 7

Now,

a1/a2 = 3/2

b1/b2 = 2/-3 = -2/3

c1/c2 = 5/7

As we can see that,

a1/a2 ≠ b1/b2

This equation represent only one solution.

Therefore, these equations are consistent.

# Consistent equations are those equations which atleast have one solution.

$\huge\mathbb{Hope \ this \ helps.}$

Answer 2

Answer:

The equation pairs are consistent

Step-by-step explanation:

Given equation : $3x + 2y = 5\\2x - 3y = 7$  , a1 = 3, a2 = 2, b1 = 2 and b2 = -3

To find : Whether the equation is consistent or inconsistent

Concept : A consistent system of equations has at least one solution, and an inconsistent system has no solution.

$for \left \{ {{a_{1}x + b_{1}x + c_{1} = 0} \atop {a_{2}x + b_{2}x + c_{2} = 0}} \right.$

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ , the equation pair is consistent

Solution :

now putting in the equation below

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

$\frac{3}{2} \neq \frac{2}{-3}$

Hence, the equation has one solution

Therefore, these equations are consistent.

#SPJ2