if the points A(3,5) and B(1,4) lie on the graph of the line ax+by=7 find the values of A and - Maths - Linear Equations in Two Variables

Question

if the points A(3,5) and B(1,4) lie on the graph of the line
ax+by=7 find the values of A and B?

Aakash Sharma · Accepted Answer

For the points A (3, 5) and B (1, 4) to lie on the graph of line ax + by = 7 must satisfy the given equation

So for x = 3 and y = 5

3a + 5b = 7 .................(1)

for x =1 and y = 4

a + 4b = 7

⇒ a = 7 – 4b ................(2)

putting the value of a from (2) in (1) we get

3(7 – 4b) + 5b = 7

21 – 12b + 5b = 7

–7b = 7 – 21 = – 14

$\Rightarrow b = \frac{14}{7} = 2$

Putting the value of b in (2) we get

a = 7 – 4 × 2 = – 1

Hence the values of a and b are – 1 and 2

if the points A(3,5) and B(1,4) lie on the graph of the line ax+by=7.find the values of A and B?