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3 years ago

For which value of a does the following system of equations have no solution? -x+6y=7 , -5x+10ay=32

Mathematics

1 answer:

dlinn [17]3 years ago

8 0

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

================

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)

===============

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

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