Asked by Person
                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
            
        -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
                    Answered by
            Person
            
    I meant to type it algebra... whoops!
    
                    Answered by
            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.
    
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.
                    Answered by
            Person
            
    So what are the number of solutions?
    
                    Answered by
            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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