SOLUTION: give the slope and y-intercept for each equation and then the number of solutions for the system: x + 200y = -30 10x - 70y = 100 I have attempted to solve this by first solvin

Algebra ->  Linear-equations -> SOLUTION: give the slope and y-intercept for each equation and then the number of solutions for the system: x + 200y = -30 10x - 70y = 100 I have attempted to solve this by first solvin      Log On


   

Question 965172: give the slope and y-intercept for each equation and then the number of solutions for the system:
x + 200y = -30
10x - 70y = 100
I have attempted to solve this by first solving for y, and then inputting y into the equations, but my "y" doesn't seem right...I came up with y = -400/270... I didn't go further because it didn't seem correct
Found 3 solutions by josgarithmetic, josmiceli, lwsshak3:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x+%2B+200y+=+-30%2C10x+-+70y+=+100%29

system%28200y=-x-30%2Cx-7y=10%29

system%28y=-x%2F200-3%2F20%2C-7y=-x%2B10%29

highlight%28system%28y=-x%2F200-3%2F20%2Cy=x%2F7-10%2F7%29%29

The each line has different slope; one being -1%2F200 and the other being 1%2F7, which are not equal.
The system of equations has ONE intersection point.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +x+%2B+200y+=+-30+
(2) +10x+-+70y+=+100+
------------------------
(2) +x+-+7y+=+10+
Add +7y+ to both sides
(2) +x+=+7y+%2B+10+
Subtract +10+ from both sides
(2) +x+-+10+=+7y+
Divide both sides by +7+
(2) +%28+1%2F7+%29%2Ax+-+10%2F7+=+y+
Write it the other way
(2) +y+=+%281%2F7%29%2Ax+-+10%2F7+
slope = +1%2F7+
y-intercept = +-10%2F7+
----------------------------
(1) +x+%2B+200y+=+-30+
Subtract +x+ from both sides
(1) +200y+=+-x+-+30+
Divide both sides by +200+
(1) +y+=+-%28+1%2F200+%29%2Ax+-+3%2F20+
slope = +-1%2F200+
y-intercept = +-3%2F20+
-------------------------------
(1) +x+%2B+200y+=+-30+
(2) +x+-+7y+=+10+
Subtract (2) from (1)
(1) +x+%2B+200y+=+-30+
(2) +-x+%2B+7y+=+-10+
-----------------------
+207y+=+-40+
+y+=+-40%2F207+
Plug this result back into (2)
(2) +-x+%2B+7%2A%28+-40%2F207%29+=+-10+
Multiply both sides by +-1+
and subtract +280%2F207+ from both sides
(2) +x+=+10+-+280%2F207+
(2) +x+=+2070%2F207+-+280%2F207+
(2) +x+=+1790%2F207+
------------------------
The solution seems to be:
( 1790/207 , -40/207 )
check my math


Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
give the slope and y-intercept for each equation and then the number of solutions for the system:
x + 200y = -30
200y=-x-30
y=-x/200-30/200
slope=-1/200; y-intercept=-30/200
..
10x - 70y = 100
70y=10x-100
y=10x/70-100/70
slope=1/7; y-intercept=-100/70
..
-x/200-30/200=10x/70-100/70
-x/200-3/20=x/7-10/7
lcd:7*200
-7x-210=200x-2000
207x=1790
x=1790/207≈8.6473
y=-(x+30)/200≈-0.1932
point of intersection: (8.6473,-0.1932)