Question

2x+3y=5 and 3x+2y=7 has...... solutions​

Answer 1

2x + 3y = 5 , 3x + 2y = 7

a1 = 2, b1 = 3, c1 = 5

a2 = 3, b2 = 2 , c2 = 5

Here,

a1/a2 ≠ b1/b2

So,

Following pair of linear equations in two variables will have 1 unique solution.

Answer 2

Answer:

Unique solution.

Step-by-step explanation:

Given: System of equation $2x+3y=5$ and $3x+2y=7$.

To determine number of solution.

Recall: For system of equation $\begin{aligned}&a_{1} x+b_{1} y+c_{1}=0 \\&a_{2} x+b_{2} y+c_{2}=0\end{aligned}$ the system has :

1. unique solution if $\left(a_{1} / a_{2}\right) \neq\left(b_{1} / b_{2}\right)$
2. infinite solution if $\left(a_{1} / a_{2}\right)=\left(b_{1} / b_{2}\right)=\left(c_{1} / c_{2}\right)$
3. no solution if $\left(a_{1} / a_{2}\right)=\left(b_{1} / b_{2}\right) \neq\left(c_{1} / c_{2}\right)$

In the given system, $a_{1} =2,b_{1}=3,c_{1}=-5,a_{2}=3,b_{2}=2,c_{2}=-7$

Here, $\frac{a_{1} }{a_{2} } =\frac{2}{3} , \frac{b_{1} }{b_{2} } =\frac{3}{2}$

Clearly $\left(a_{1} / a_{2}\right) \neq\left(b_{1} / b_{2}\right)$ hence system has unique solution.

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