The statement - The graph of a system of equations with the same slope and the same y intercepts will have no solution is True
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.
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.
Graph the equation then find the x intercepts.
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.
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.
so you can find the solution for the x-values. the x-intercepts are when the graph crosses the x-axis
Graph both equations on the same graph. Where they intersect is the solution to the system of equations
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.
It represents the point of intersection on a graph.
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.
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.
parallel
Graph the equation then find the x intercepts.
point-slope formula and finding the slope of the line.
Yes - provided you allow both x and y intercepts.
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.
coordinate planes, intercepts, #'s, ordered pairs..etc.