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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.
When we look for a solution for a system of equations or inequalities are we looking into an AND situation or an OR situation?
Unless otherwise stated, the "AND" case is normally assumed, i.e., you have to find a solution that satisfies ALL equations.
How would you know if a linear system has a solution?
One way is to look at the graphs of these equations. If they intersect, the point of intersection (x, y) is the only solution of the system. In this case we say that the system is consistent. If their graphs do not intersect, then the system has no solution. In this case we say that the system is inconsistent. If the graph of the equations is the same line, the system has infinitely simultaneous solutions. We can use several methods in order to solve the system algebraically. In the case where the equations of the system are dependent (the coefficients of the same variable are multiple of each other), the system has infinite number of solutions solution. For example, 2x + 3y = 6 4y + 6y = 12 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. Try to solve this system of equations, 2x + 3y = 6 4x + 6y = 7 If you use addition or subtraction method, and you obtain a peculiar result such that 0 = 5, actually you have shown that the system has no solution (there is no point that satisfying both equations). When you use the substitution method and you obtain a result such that 5 = 5, this result indicates no solution for the system.
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..
How many solution does a system of equation with lines of same slope and y-intercept have?
Two lines with the same slope and y-intercept look like one single line. The "system" of equations consists of the same equation twice. The lines coincide at every point, which means there are an infinite number of solutions.
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 look like?
A solution is clear.
Solutions look like what?
Solution = (your solution here)
What does a system of equation with no solution look like?
Functions (lines, parabolas, etc.) whose graphs never intersect each other.
How do you find x and y in system of equations?
The basic idea here is to look at both equations and solve for either x or y in one of the equations. Then plug the known value into the second equation and solve for the other variable.
Can you give me an example of an infinite solution to an equation?
The common one is a line. y=mx+b Let's look at the line y=2x+4 This is a line with slope 2 and y intercept 4. The solutions will be all the points on that line and there are an infinite number of them. If x=0, y=4 if x=1, y=6 etc Now you could also look at a system of equations, y=2x+4 and 2y=4x+8. Since these in fact represent the same line, one again the solution is infinite. This is a trivial example just to show you how an infinite number of points can be the solution to 1 or more equations.
What does a graph with infinitely many solutions look like?
they have same slop.then two linear equations have infinite solutions
