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
Answer:
a = [tex]\frac{3}{11}[/tex] , b = [tex]\frac{2}{11}[/tex]
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 = [tex]\frac{2}{11}[/tex]
Substitute this value into (1) and solve for a
a + 4([tex]\frac{2}{11}[/tex] ) = 1
a + [tex]\frac{8}{11}[/tex] = [tex]\frac{11}{11}[/tex] ( subtract [tex]\frac{8}{11}[/tex] from both sides )
a = [tex]\frac{11}{11}[/tex] - [tex]\frac{8}{11}[/tex] = [tex]\frac{3}{11}[/tex]
