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?

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(6628) (Show Source): You can put this solution on YOUR website!
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:

Substituting into second equation:

so and from first equation

Using third equation: so

Substituting into fourth equation:

so and from third equation

The ratio of a to b is 19:45
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