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You know that equations and inequalities have different solution symbols, therefore, how many solutions will each one of them have when solving for the variable?
50
What else can I help you with?
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.
Are there any solutions to these inequalities y-5x plus 2 and y-5x-3?
No, there are not, and here's why: to solve for this kind of problem, you will need to set both equations equal to each other. This will give you y - 5x + 2 = y - 5x - 3, You can subtract a y and a -5x from both sides, and this will leave you with 2 = -3, which is, of course, an impossibility. There are therefore no solutions to these inequalities.
Do Radical equations sometimes have extraneous solutions?
Yes, radical equations can sometimes have extraneous solutions. When solving these equations, squaring both sides to eliminate the radical can introduce solutions that do not satisfy the original equation. Therefore, it is essential to check all potential solutions in the original equation to verify their validity.
How many solutions are there for a system of two quadratic inequalities?
The number of solutions for a system of two quadratic inequalities can vary widely, depending on the specific inequalities involved. They may have no solutions, a finite number of solutions, or infinitely many solutions. Graphically, the solutions correspond to the regions where the corresponding quadratic curves intersect and how they relate to each inequality. Therefore, analyzing each inequality's graph is crucial to determining the solution set.
The two lines graphed below are parallel How many solutions are there to the system of equations?
Although there is no graph, the number of solutions is 0.
Can a system of two linear equations have exactly two solutions explain?
No, a system of two linear equations cannot have exactly two solutions. In a two-dimensional space, two linear equations can either intersect at one point (one solution), be parallel (no solutions), or be the same line (infinitely many solutions). Therefore, it is impossible for a system of two linear equations to have exactly two solutions.
How do you solve identities on trigonometry?
Unlike equations (or inequalities), identities are always true. It is, therefore, not possible to solve them to obtain values of the variable(s).
Why could a system of linear equations have two solutions?
A system of linear equations cannot have two distinct solutions if it is consistent and defined in a Euclidean space. If two linear equations intersect at a single point, they have one solution; if they are parallel, they have no solutions. However, if the equations are dependent, meaning one equation is a multiple of the other, they represent the same line and thus have infinitely many solutions, not just two. Therefore, in standard scenarios, a system of linear equations can either have one solution, no solutions, or infinitely many solutions, but not exactly two.
Provide a system of TWO equations in slope-intercept form with no solutions how to explain why this system has no solutions?
y = mx + b y = mx + c c does not equal b the two equations are parallel and will therefore never intersect with one another.
What are equations with the same solution?
Equations with the same solution are called dependent equations, which are equations that represent the same line; therefore every point on the line of a dependent equation represents a solution. Since there is an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 2x + y = 8 4x + 2y = 16 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. A system of linear equations is consistent if there is only one solution for the system. A system of linear equations is inconsistent if it does not have any solutions.
Does this system of equations have one solution no solutions or an infinite number of solutions 2x - y equals 8 and x plus y equals 1?
Solve both equations for y, that is, write them in the form y = ax + b. "a" is the slope in this case. Since the two lines have different slopes, when you graph them they will intersect in exactly one point - therefore, there is one solution.
Does 2x y 5 system of equations have one solution no solutions or an infinite number of solutions?
Well, honey, let me break it down for you. The system of equations 2x=y and 5=5 is a case of parallel lines that will never intersect, meaning there are no solutions. So, in simpler terms, these equations ain't gonna be holding hands and skipping down the solution lane together.
