if(2,3) and (4,0) lie on the graph of equation ax+by=1 find the value of a and b and plot - Maths - Linear Equations in Two Variables

Question

if(2,3) and (4,0) lie on the graph of equation ax+by=1 find the
value of a and b and plot the graph of the equation obtained

Harleen Birdi · Accepted Answer

(2,3) and (4,0) lie on ax + by = 1 âˆ´ (2,3) and (4,0) will satisfy ax + by = 1 $\Rightarrow a (2) + b (3) = 1 and a (4) + b (0) = 1 \Rightarrow 2 a + 3 b = 1 and 4a = 1 \Rightarrow a = \frac{1}{4} \Rightarrow 2 (\frac{1}{4}) + 3 b = 1 \Rightarrow \frac{1}{2} + 3 b = 1 \Rightarrow 3 b = 1 - \frac{1}{2} \Rightarrow 3 b = \frac{1}{2} \Rightarrow b = \frac{1}{6} Hence, a = \frac{1}{4} and b = \frac{1}{6}$ âˆ´ Equation becomes $(\frac{1}{4}) x + (\frac{1}{6}) y = 1$ $\Rightarrow \frac{x}{4} + \frac{y}{6} = 1 \Rightarrow \frac{3 x + 2 y}{12} = 1 \Rightarrow 3 x + 2 y = 12$ $\Rightarrow y = 6 (1 - \frac{x}{4}) = \frac{3}{2} (4 - x) (1) When x = 0 \Rightarrow y = 6 When x = 2 \Rightarrow y = 3 When x = 4 \Rightarrow y = 0$ We get the table as follows: x 0 2 4 y` 6 3 0 Plotting the graph:

if(2,3) and (4,0) lie on the graph of equation ax+by=1. find the value of a and b and plot the graph of the equation obtained