Question

The straight line ax+by=1passes through the points (1,4)and (3,1).Find the values of a and b?

Answer 1

Answer:

a = $\frac{3}{11}$ , b = $\frac{2}{11}$

Step-by-step explanation:

Substitute (1, 4) and (3, 1) into the equation

a + 4b = 1 → (1)

3a + b = 1 → (2)

Multiplying (1) by - 3 and adding to (2) will eliminate a

- 3a - 12b = - 3 → (3)

Add (2) and (3) term by term to eliminate a

0 - 11b = - 2

- 11b = - 2 ( divide both sides by - 11 )

b = $\frac{2}{11}$

Substitute this value into (1) and solve for a

a + 4($\frac{2}{11}$ ) = 1

a + $\frac{8}{11}$ = $\frac{11}{11}$ ( subtract $\frac{8}{11}$ from both sides )

a = $\frac{11}{11}$ - $\frac{8}{11}$ = $\frac{3}{11}$

Answer 2

Answer:

a= 3/11

b = 2/11

Step-by-step explanation:

a(1) + b(4) = 1

a + 4b = 1

a(3) + b(1) = 1

3a + b = 1

b = 1-3a

a + 4(1-3a) = 1

a+ 4-12a = 1

-11a = -3

a = 3/11

b = 1-3(3/11)

b= 2/11