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Functions (lines, parabolas, etc.) whose graphs never intersect each other.
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When will be the linear equations a1x plus b1y plus c1 equals 0 and a2x plus b2y plus c2 equals 0 has unique solution?
When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..
Does every pair of linear simultaneous equations have a unique solution?
So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.
What do quadratic equations look like?
ax2 + bx + c
What does a solution set look like in algebra?
r-20=-26
Is it impossible for a system of equations in which one of the lines is a horizontal line to have a solution?
No it is not impossible, as long as only one of the lines is horizontal. Since you are referring to lines, it sounds like a 2-variable system (with x and y, for example). An example would be something like [in a word problem]: find two numbers, whose sum is 12; and one of the numbers is 5. So the numerical system could look something like:x + y = 12 and y = 5. The y = 5 is a horizontal line. To solve, just plug y=5 into the first equation, and solve for x=7, so the point of intersection is (7,5). As long as the two lines are not parallel, there will be a solution.
