Remark
If the lines are parallel, there are no solutions to the system of equations. Start with the equation you know the most about.
x + 6y = 7 Subtract x from both sides
x - x + 6y = 7 - x Combine
6y = - x + 7 Switch and divide by 6
y = -x / 6 + 7/6
The general equation for a line is y = mx + b where m is the slope of the line.
m = - 1/6
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Now look at the second equation
10ay - 5x = 32 Add 5x to both sides
10ay = 5x + 32 Divide by 10a
y = (5/10a)x + 32/(10a)
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Now you must make
5/10a = - 1/6 Cross Multiply
5* 6 = - 10a * 1
30 = - 10a Divide by - 10
a = 30 / - 10
a = - 3
So these two equations will have no solution when a = - 3
