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Can two perpendicular equations have different y-intercepts?
If 2 equations are perpendicular to one another they can have different y-intercepts, depending on how they are situated on a (x,y) graph.
Does the graph of a system of equations with different slopes have no solutions?
The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.
How do you use a graphing calculator to solve quadratic equations?
Graph the equation then find the x intercepts.
On a graph the solution of a system of a linear equations will be represented by what?
The set of points the graphed equations have in common. This is usually a single point but the lines can be coincident in which case the solution is a line or they can be parallel in which case there are no solutions to represent.
Can you solve system of equations by graphing?
Yes you can, if the solution or solutions is/are real. -- Draw the graphs of both equations on the same coordinate space on the same piece of graph paper. -- Any point that's on both graphs, i.e. where they cross, is a solution of the system of equations. -- If both equations are linear, then there can't be more than one such point.
Why do you need x intercepts for quadratic equations?
so you can find the solution for the x-values. the x-intercepts are when the graph crosses the x-axis
Can two perpendicular equations have different y-intercepts?
If 2 equations are perpendicular to one another they can have different y-intercepts, depending on how they are situated on a (x,y) graph.
What does a single solution to a system of equations mean?
It represents the point of intersection on a graph.
Does the graph of a system of equations with different slopes have no solutions?
The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.
How can graphs be used to estimate the solution for a system of linear equations?
Graphs can be used in the following way to estimate the solution of a system of liner equations. After you graph however many equations you have, the point of intersection will be your solution. However, reading the exact solution on a graph may be tricky, so that's why other methods (substitution and elimination) are preferred.
If a system of linear equations has no solution then the graph of the two equationsmust be what kind of line?
parallel
When solving a system of equations by graphing you will need to graph the equations on the same?
When solving a system of equations by graphing, you will need to graph the equations on the same coordinate plane. This allows you to visually identify the point where the two lines intersect, which represents the solution to the system. If the lines intersect at a single point, that point is the unique solution; if the lines are parallel, there is no solution; and if they coincide, there are infinitely many solutions.
How do you interpret the solution of a system of equations by the corresponding graph?
The solution of a system of equations corresponds to the point where the graphs of the equations intersect. If the equations have one unique point of intersection, that point represents the solution of the system. If the graphs are parallel and do not intersect, the system has no solution. If the graphs overlap and coincide, the system has infinitely many solutions.
How do you use a graphing calculator to solve quadratic equations?
Graph the equation then find the x intercepts.
When you graph a system of linear equations why does the intersection of the two lines represent the solution of the system?
The intersection of two lines in a graph of a system of linear equations represents the solution because it is the point where both equations are satisfied simultaneously. At this point, the x and y coordinates meet the conditions set by both equations, meaning that the values of x and y make both equations true. Hence, the intersection point is the unique solution to the system, assuming the lines are not parallel or coincident.
The solution to a two-variable system is the point on a graph at which the lines cross?
Yes, the solution to a two-variable system is the point where the equations of the lines representing the system intersect on a graph. This point represents the values of the variables that satisfy both equations simultaneously.
Can all the linear equations be graph using the intercept?
Yes - provided you allow both x and y intercepts.
