SOLUTION: im having trouble with these can someone help. determine from the slopes and y-intercepts of the two lines whether the linear equations that name those lines are inconsistent,consi

Question 148507: im having trouble with these can someone help. determine from the slopes and y-intercepts of the two lines whether the linear equations that name those lines are inconsistent,consistant,or dependent. if the equations are consistant,find the common solutionof that system of equations. 1. y=5x+3 5x-y=7 2. 3x-2y=5 2y=3x+7 3. x-3y=13 3x=9y+39 4. x+4/5y=4 x-1/2y=-9
Answer by mangopeeler07(462) (Show Source): You can put this solution on YOUR website!
1. y=5x+3 5x-y=7

Substitute 5x+3 for y in the second equation
5x-(5x+3)=7

Simplify
5x-5x-3=7

-3=7
**no solution**
---------------------------------------------------------------
2. 3x-2y=5 2y=3x+7

Plug in 3x+7 for 2y
3x-(3x+7)=5

Simplify
3x-3x-7=5

-7=5
**no solution**
---------------------------------------------------------------
3. x-3y=13 3x=9y+39
Multiply the first equation by 3.
3(x-3y=13) 3x=9y+39

3x-9y=39 3x=9y+39

Add 9y to both sides in the first equation

3x=9y+39 3x=9y+39
**infinitely many solutions**
----------------------------------------------------------------
4.x+4/5y=4 x-1/2y=-9

Subtract the second equation from the first
1.3y=13
y=10

Plug 10 in for y in the first equation
x+4/5(10)=4
or

x+8=4
x=-4

So **y=10 and x=-4.**
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