Question:
The linear equation 3x − 5y = has
(a) a unique solution
(b) two solutions
(c) infinitely many solutions
(d) no solution
Solution:
(c) infinitely many solutions
Given linear equation: $3 x-5 y=15$
Or, $x=\frac{5 y+15}{3}$
When $y=0, x=\frac{15}{3}=5$.
When $y=3, x=\frac{30}{3}=10$.
When $y=-3, x=\frac{0}{3}=0$
Thus, we have the following table:
Plot the points $A(5,0), B(10,3)$ and $C(0,-3)$. Join the points and extend them in both the directions.
We get infinite points that satisfy the given equation.
Hence, the linear equation has infinitely many solutions.
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