Drag the tiles to the correct boxes to complete the pairs.
Match each system of linear equations with the correct number of solutions.
No solution
One solution
Infinitely many solutions
3x - y = 4
6x - 2y = 8
-3x + y = 7
2x - 4y = -8
y = -4x - 5
y = -4x +1
Answers
Given:
a.) 3x - y = 4
6x - 2y = 8
b.) -3x + y = 7
2x - 4y = -8
c.) y = -4x - 5
y = -4x +1
To Find:
The number of solutions for given three system of linear equations.
Solution:
We can simply solve this numerical problem by using the following process.
Concept:
Let the system of equations be a₁x + b₁y = c₁ and a₂x + b₂y = c₂ then
Condition for One solution: a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂
Condition for No Solution: a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Condition for infinitely many solutions: a₁/a₂ = b₁/b₂ = c₁/c₂
Now in the given question:
a.) 3x - y = 4
6x - 2y = 8
⇒ a₁/a₂=3/6 = 1/2 ; b₁/b₂ = -1/-2 = 1/2 ; c₁/c₂ = 4/8 = 1/2
⇒ a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2
The given system of equations is coincident lines, hence has infinitely many solutions.
b.) -3x + y = 7
2x - 4y = -8
⇒ a₁/a₂= -3/2 ; b₁/b₂ = 1/-4 ; c₁/c₂ = 7/-8
⇒ a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂
The given system of equations is intersecting lines, hence having a single solution.
c.) y = -4x - 5
y = -4x +1
⇒ a₁/a₂= -4/-4 = 1 ; b₁/b₂ = 1/1 = 1 ; c₁/c₂ = -5/1 = -5
⇒ a₁/a₂ = b₁/b₂ ≠ c₁/c₂
The given system of equations is parallel lines, hence having no solution.
#SPJ2
Answer:
Step-by-step explanation: