Question

How many solutions does the system of equations have?

-2x=-10y+6; x+5y=3

1
2
infinitely many
none


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

1
2
infinitely many
none



y-7x=-14; 7y-49x=-2

1
2
infinitely many
none

Answers

Person
I meant to type it algebra... whoops!
Reiny
Here is a quick way to find the slope of a line,
if written in the form Ax + By + C = 0
the slope of the line is -A/B

so for #1
-2x=-10y+6 ---> 2x - 10y + 6 = 0 , slope = -2/-10 = 1/5
x+5y=3 ---- slope = -1/5

so the lines have different slope, so they must intersect in 1 point.

#2
y=4x+3 in the form y = mx + b so the slope is 4


2y-8x=3 ---> 8x - 2y + 3 = 0 , slope is -2/-8 = 1/4
again, different slopes, so 1 solution

do the last one the same way.
Person
So what are the number of solutions?
Damon
If they have the same slope they are parallel and never cross unless they also have the same constant and are identical in which case they sit on top of each other and have an infinite number, the same y for very x

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