Find whether this pair of equations has a unique solution or an infinite number of solutions or no solution: $3x+5y=13$, $5x+3y=4$.
Given: Pair of equations $3x+5y=13$, $5x+3y=4$.
To do: To find whether this pair of equations has a unique solution or an infinite number of solutions or no solution.
Solution:
Given equations are:
$3x+5y=13\ or\ 3x+5y-13=0$, $5x+3y=4\ or\ 5x+3y-4=0$
On comparing with General form of a pair of linear equations in two variables $x$ & $y$ is:
$a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2= 0$
$a_1=3,\ b_1=5,\ c_1=-13$
$a_2= 5,\ b_2=3,\ c_2=-4$
$\frac{a_1}{a_2}= \frac{3}{5},\ \frac{b_1}{b_2}=\frac{5}{3},\ \frac{c_1}{c_2}=\frac{-13}{-4}=\frac{13}{4}$
Here, $\frac{a_1}{a_2}
eq \frac{b_1}{b_2}$
Hence, this pair of equations has unique solution.
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