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How are the graphs of systems of linear equations and inequalities related to their solutions?
The graphs of systems of linear equations represent the relationships between variables, with each line corresponding to an equation. The point(s) where the lines intersect indicate the solution(s) to the system, showing where the equations are satisfied simultaneously. For systems of linear inequalities, the graphs display shaded regions that represent all possible solutions that satisfy the inequalities; the intersection of these regions highlights the feasible solutions. Therefore, both the graphs and their intersections are crucial for understanding the solutions to the systems.
Do all graphs of linear equations have x intercepts?
YES, all linear equations have x-intercepts. because of the x, y has to be there 2!
How do you differentiate linear inequalities in two variables from linear equations in two variables?
Linear inequalities in two variables involve expressions that use inequality symbols (such as <, >, ≤, or ≥), while linear equations in two variables use an equality sign (=). The solution to a linear equation represents a specific line on a graph, while the solution to a linear inequality represents a region of the graph, typically shaded to show all the points satisfying the inequality. Moreover, linear inequalities allow for a range of values, whereas linear equations specify exact values for the variables.
If two linear equations are in standard form how can you tell that the graphs are parellel?
If the slopes are the same on both graphs, they are parallel, and will never touch.
What is the difference between the solution of a system of linear inequalities and the solution of a system of linear equations?
The solution of a system of linear equations consists of specific points where the equations intersect, typically yielding a unique point, infinitely many points, or no solution at all. In contrast, the solution of a system of linear inequalities represents a region in space, encompassing all points that satisfy the inequalities, often forming a polygonal shape in two dimensions. While equations define boundaries, inequalities define areas that can include multiple solutions. Thus, the nature of their solutions differs fundamentally: precise points versus expansive regions.
How are the graphs of systems of linear equations and inequalities related to their solutions?
The graphs of systems of linear equations represent the relationships between variables, with each line corresponding to an equation. The point(s) where the lines intersect indicate the solution(s) to the system, showing where the equations are satisfied simultaneously. For systems of linear inequalities, the graphs display shaded regions that represent all possible solutions that satisfy the inequalities; the intersection of these regions highlights the feasible solutions. Therefore, both the graphs and their intersections are crucial for understanding the solutions to the systems.
Why is it important the linear equations and inequalities?
There are many simple questions in everyday life that can be modelled by linear equations and solved using linear programming.
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.
How are linear inequalities and linear equations the same?
They are not. An inequality cannot, by definition, be the same as an equation.
Do all graphs of linear equations have x intercepts?
YES, all linear equations have x-intercepts. because of the x, y has to be there 2!
Does in linear graphs the slope of the line change with the x-coordinate?
No. A linear graph has the same slope anywhere.
Who made linear equations?
Descartes made the coordinate plane.
What types of equations or inequalities describe points x y that lie on a circle?
Linear equations or inequalities describe points x y that lie on a circle.
How linear equations were used for the first time?
Rene Descartes was a French mathematician who created the coordinate plane on which linear equations are plotted.
Can there be more than one point of intersection between the graphs of two linear equations?
Normally no. But technically, it is possible if the two linear equations are identical.
How are line graphs relates to math?
they express linear equations in a visible way
What outcome is not possible for the graph of a system of two linear equations?
the equation graphs
