SOLUTION: The lines described by 3x-y=17, 2x+5y=17, x+2y=a+b, and x-y=3b-5a all pass through the same point. What is the ratio of a to b?

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: The lines described by 3x-y=17, 2x+5y=17, x+2y=a+b, and x-y=3b-5a all pass through the same point. What is the ratio of a to b?      Log On

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Question 74478: The lines described by 3x-y=17, 2x+5y=17, x+2y=a+b, and x-y=3b-5a all pass through the same point. What is the ratio of a to b?
Answer by scott8148(5891) About Me  (Show Source):
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At that point, the x and y values are the same in all the equations. Using the first two equations, you can find values for x and y; and then use those values in the third and fourth equations to find a and b.

From first equation: y=3x-17

Substituting into second equation: 2x%2B5%2A%283x-17%29=17

so x=6 and from first equation y=1

Using third equation: 8=a%2Bb so a=8-b

Substituting into fourth equation: 5=3b-5%2A%288-b%29

so b=45%2F8 and from third equation a=19%2F8

The ratio of a to b is 19:45