# Infinite Solutions

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• Nov 3rd 2008, 03:05 PM
mjp1991
Infinite Solutions
So I had to solve systems and if the system has an infinite solution set, we had to give three solutions for it. However, I'm not really sure how to get these solutions, please help!

x+y=4(y+2)
x-y=2(y+4)

x+y=4y+8
x-y=2y+8
x-3y=8
x-3y=8

-x+3y=-8
x-3y=8
0=0

Thanks =)
• Nov 4th 2008, 05:49 AM
earboth
Quote:

Originally Posted by mjp1991
So I had to solve systems and if the system has an infinite solution set, we had to give three solutions for it. However, I'm not really sure how to get these solutions, please help!

x+y=4(y+2)
x-y=2(y+4)

x+y=4y+8
x-y=2y+8
x-3y=8
x-3y=8

-x+3y=-8
x-3y=8
0=0

Thanks =)

All your considerations and calculations are OK.

The elements of the solution set are pairs of numbers with the property \$\displaystyle y=\dfrac13 x - \dfrac83\$

You only have to choose for some x-values, calculate the corresponding y-values and that's it:

For instance: (-1, -3); (2,-2); (8, 0)