Question

the pair of equation 2x+3y=5 and 3x+2y=5 has​

Answer 1

Answer:

2x+3y=5

-(3x+2y)=-5

=-x+y=0

=y=x eq(1)

sustitute eq(1) in 2x+3y=5

2x+3x=5

5x=5

=x=1

Therefore x=1 =y

Answer 2

QUESTION:

the pair of equation 2x+3y=5 and 3x+2y=5 has which type solution? $\red{(complete question)}$

ANSWER:

We used the formula here;

1.For no solution

$\frac{a1}{a2} = \frac{b1}{b2} \: not \: equal \: to \: \frac{c1}{c2}$

2. For many solution

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

3..For unique solution

$\frac{a1}{a2} not \: equal \: to \: \frac{b1}{b2}$

now come to main question;

$2x + 3y - 5......(eq.1)$

it is in the form of

$a1x1 +b1 y1 + c1 = 0$

$3x + 2y - 5 = 0$

It is in the form of

$a2x2 + b2y2 + c2 = 0$

so;

a1 = 2| b1 = 3 | c1 = -5

a2 = 3| b2 = 2 | c2 = -5

now,

$\frac{a1}{a2} = \frac{2}{3}$

$\frac{b1}{b2} = \frac{3}{2}$

$\frac{c1}{c2} = \frac{ - 5}{ - 5}$

$\huge\pink{it has a unique solution;}$

because;

$\frac{a1}{a2} is \: nt \: equal \: to \frac{b1}{b2}$

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