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The general equation for a line is y=ax+b, right? If two lines are to never coincide, they have to be parallelle, stretching both ways to infinity wihtout meeting.
So if you put both your equations on the general form, getting this:
y1=ax+b
y2=cx+d
The only way these lines are parallelle is if a=c. So whenever a differs from c, your line will coincide at some point. (to find this point, set y1 = y2 and solve the equation for x, giving you the x-value for their point of coincision).
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How do you know if two lines are intersecting lines with out graphing?
For two dimensional lines: Get the formulas for the two lines into a format so that you can evaluate the slope. If the slopes are different, then they will intersect. If the slopes are the same, then you have two parallel lines, or possibly, the two equations describe the same line.
How do you find the intersection of 2 lines in space?
By solving simultaneous linear equations. (If you don't know how to do this, it's a bit more complicated than can be detailed here, but basically you cast the equations for the two lines into the form ax + by = z and then see if there are any valid solutions to the equation a1x + b1y = a2x + b2y. If so, that's your answer. If not, the lines are skew and do not intersect.)
Where do you use formulating equations in life?
well, if you know all the formulating equations it will make you better at regular equations and regular equations can be used in everyday life
How do you solve linear equations?
I DON'T KNOW...... TEACH ME!!?!?!?!?!?!
How do yo know A system of two linear equations is dependent and consistent?
There are several ways to find this out; for example, assuming the equations are in "x" and "y", and you put the equation in slope-intercept form (solve them for "y"), they will have different slopes. There is also a method based on determinants - some determinant must be non-zero.
