Two lines are parallel. Do the equations of those lines represent a consistent system, an inconsistent system,

Question

Two lines are parallel. Do the equations of those lines represent a consistent system, an inconsistent system, or a dependent system? How many solutions will such a system have? Why?

Answer 1

slope form
Y=mx+b

basically, 2 lines are parallel, which means they have the same slope (m)=1/2

A. y1=1/2x+5
B. y2=1/2x+10

They are two different lines;
A. crosses the Y axis at (0,5) x,y
crosses the X axis at (-20,0)
B. crosses the Y axis at (0,10) x,y
crosses the X axis at (-10,0)

These are inconsistent because each equation has 1 solution when you set and they will never have the SAME solution because the never meet (intersect).
y1=0 for A. you get 5
you set
y2=0 for B. you get 10

Answer 2

we ought to apply a gadget of two equations with unequal coefficient ratios to make the answer unique. So, as an occasion, we ought to apply a gadget of the type x + y = some consistent x - y = yet another consistent because of the fact the coefficient ratios a million:a million and a million:-a million are unequal. Then we are able to plug in -a million for x and four for y to get the wonderful ideal-hand-factor constants. on condition that -a million + 4 = 3 and -a million - 4 = -5, the gadget x + y = 3 x - y = -5 might artwork. Lord bless you immediately!

Answer 3

They form an inconsistent system because there is no solution for an intersection of the two lines.