Question

For what value of a and b the points 2,3.and 4,0.lie on the graph of the equation ax+ by =7

Answer 1

Dear Student,

(2,3) and (4,0) lie on the line ax + by = 7
Therefore, (2,3) and (4,0) soud satisfy the equation ax + by = 7

Substituting (2,3) in ax + by = 7 : 2a + 3b = 7 ..[1]

Substituting (4,0) in ax + by = 7 : 4a + 0b = 7
or 4a = 7
$\to a=\frac{7}{4}$

Substituting the value of a in [1] :
$$\begin{gathered} 2*\frac{7}{4}+3b=7 \\ \to \frac{7}{2}+3b=7 \\ \to 3b=7-\frac{7}{2} \\ \to 3b=\frac{14-7}{2} \\ \to 3b=\frac{7}{2} \\ \to b=\frac{7}{6} \\ Hence,a=\frac{7}{4}andb=\frac{7}{6} \\ / \end{gathered}$$


Regards