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How many solution does a system of equation with lines of same slope and y-intercept have?
Wiki User
∙ 11y ago
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.
Wiki User
∙ 11y ago
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What does a system of equation with no solution look like?
Functions (lines, parabolas, etc.) whose graphs never intersect each other.
When the equation in a linear system have different slopes then the system has what kind of solution?
It is not possible to tell. The lines could intersect, in pairs, at several different points giving no solution. A much less likely outcome is that they all intersect at a single point: the unique solution to the system.
It is impossible for a system of two linear equations to have exactly one solution. True or False?
False, think of each linear equation as the graph of the line. Then the unique solution (one solution) would be the intersection of the two lines.
The graph of a system of equations with the same slope will have no solutions?
That's right. If a system of equations has a solution, then their graphs intersect, and the point where they intersect is the solution, because it's the point that satisfies each equation in the system. Straight-line graphs with the same slope are parallel lines, and they never intersect, which is another way of saying they have no solution.
Can a system of linear equation have more than one solutions?
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
The solution of a system of equation is?
the solution to a system is where the two lines intersect upon a graph.
Does every system of a linear equation have a solution?
No, if two lines are parallel they will not have a solution.
If there is no solution to a system of equations it means?
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
Why does the intersection of the two lines represent the solution of the linear equation system?
The solution to a system is an ordered pair (x,y) where the two lines intersect.
What must be true about the lines of a system of equation that has not one solution but infinitely many solutions?
There must be fewer independent equation than there are variables. An equation in not independent if it is a linear combination of the others.
Which of these number lines represents the solution to this equation?
That one, there!
What does a system of equation with no solution look like?
Functions (lines, parabolas, etc.) whose graphs never intersect each other.
When the equation in a linear system have different slopes then the system has what kind of solution?
It is not possible to tell. The lines could intersect, in pairs, at several different points giving no solution. A much less likely outcome is that they all intersect at a single point: the unique solution to the system.
How you can obtain the solution to a system of equations by graphing?
In the same coordinate space, i.e. on the same set of axes: -- Graph the first equation. -- Graph the second equation. -- Graph the third equation. . . -- Rinse and repeat for each equation in the system. -- Visually examine the graphs to find the points (2-dimension graph) or lines (3-dimension graph) where all of the individual graphs intersect. Since those points or lines lie on the graph of each individual graph, they are the solution to the entire system of equations.
It is impossible for a system of two linear equations to have exactly one solution. True or False?
False, think of each linear equation as the graph of the line. Then the unique solution (one solution) would be the intersection of the two lines.
How do you know which region of the graph of a system of linear inequalities contains the solutions?
If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.
What the system of linear equation in two variabes which has no solution?
For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.) For example y = mx + b and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution. With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.
