SOLUTION: The system of linear equations below has a unique solution for all but one value of a : 10 x - 20 y = 50 26 x + a y = 130 What is this exceptional value for a ?

Question 958102: The system of linear equations below has a unique solution for all but one value of a :
10 x - 20 y = 50
26 x + a y = 130
What is this exceptional value for a ?
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
10x-20y=50
26x+ay=130
If the two equations are equivalent, there are infinite solutions.
Divide the coefficient of x in first equation by coefficient in second: 10/26=2.6
Divide constant in first by constant in second: 50/130=2.6
They are the same, so use this factor to determine coefficient of y
(2.6)(20)=-52
This makes the second equation:
26x+(-52)y=130 so a=-52 and both equations represent the same line, so there are infinite solutions.
ANSWER: The exceptional value of a is (-52).

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