Classify each system of equations as having a single solution, no solution, or infinite solutions.
A. y = 5 − 2x
4x + 2y = 10
B. x = 26 − 3y
2x + 6y = 22
C. 5x + 4y = 6
10x − 2y = 7
D. x + 2y = 3
4x + 8y = 15
E. 3x + 4y = 17
-6x = 10y − 39
F. x + 5y = 24
5x = 12 − y
Answers
Given : A. y = 5 − 2x
4x + 2y = 10
B. x = 26 − 3y
2x + 6y = 22
C. 5x + 4y = 6
10x − 2y = 7
D. x + 2y = 3
4x + 8y = 15
E. 3x + 4y = 17
-6x = 10y − 39
F. x + 5y = 24
5x = 12 − y
To Find : Classify each system of equations as having a single solution, no solution, or infinite solutions.
Solution:
a₁x+ b₁y=c₁
a₂x+b₂y=c₂
Consistent
if a₁/a₂ ≠ b₁/b₂ ( unique solution)
a₁/a₂ = b₁/b₂ = c₁/c₂ ( infinite solution )
Inconsistent
if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ( No solution)
A.
y = 5 − 2x => 2x + y = 5
4x + 2y = 10
=> 2/4 = 1/2 = 5/10
=> 1/2 = 1/2 = 1/2
infinite solution
B.
x = 26 − 3y => x + 3y = 36
2x + 6y = 22
=> 1/2 = 3/6 ≠ 36/22
No solution
C.
5x + 4y = 6
10x − 2y = 7
=> 5/10 ≠ 4/(-2)
unique solution
D.
x + 2y = 3
4x + 8y = 15
=> 1/4 = 2/8 ≠ 3/15
No solution
E.
3x + 4y = 17
-6x = 10y − 39 => 6x + 10y = 39
=> 3/6 ≠ 4/10
unique solution
F.
x + 5y = 24
5x = 12 − y => 5x + y = 12
=> 1/5 ≠ 5/1
unique solution
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Answer:
=> 1/5 ≠ 5/1
Step-by-step explanation: