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If a system of linear of linear equations has infinitely many solutions what does this mean about the two lines?
If a system of linear equations has infinitely many solutions, it means that the two lines represented by the equations are coincident, meaning they lie on top of each other. This occurs when both equations represent the same line, indicating they have the same slope and y-intercept. As a result, any point on the line is a solution to the system.
What does it mean if there are an infinite number of solutions for a system of linear equations?
It means that the equations are actually both the same one. When they're graphed, they both turn out to be the same line.
In algebra what does it mean if a system is independent?
this means you have no more than 5 solutions in a system of equations.
Why do people call it a system when two lines intersect?
They do not. A set of lines can also be considered as a system of linear equations. But the fact that there is such a system does not mean that the lines intersect.
What situations can best be modeled by literal equations?
literal equations? maybe you mean linear equations? Please edit and resubmit your question if that is what you meant.
Can a system of two linear equations in two variables have 3 solutions?
No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions
What does it mean if there are an infinite number of solutions to a system of linear equations?
Any two numbers that make one of the equations true will make the other equation true.
What does it mean if there are an infinite number of solutions for a system of linear equations?
It means that the equations are actually both the same one. When they're graphed, they both turn out to be the same line.
What does the answer 12 equals 12 in a system of equations mean?
It probably means that one of the equations is a linear combination of the others/ To that extent, the system of equations is over-specified.
In algebra what does it mean if a system is independent?
this means you have no more than 5 solutions in a system of equations.
What does it mean to solve a system of linear equations?
Find values for each of the unknown variables (or at least as many as is possible for the system) that satisfy all the equations.
Why do people call it a system when two lines intersect?
They do not. A set of lines can also be considered as a system of linear equations. But the fact that there is such a system does not mean that the lines intersect.
What situations can best be modeled by literal equations?
literal equations? maybe you mean linear equations? Please edit and resubmit your question if that is what you meant.
What does it mean by solving linear systems?
Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.
Systems of equations with different slopes and different y-intercepts have no solutions?
No the only time that a system of equations would have no solutions is when the two equations have the same slope but different y-intercepts which would mean that they are parallel lines. However, if they have different slopes and different y-intercepts than the solution would be where the two lines intersect.
What does linear inequality mean?
A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥. It represents a range of values for which the linear expression holds true, often depicted graphically as a shaded region on one side of a line in a coordinate plane. Unlike linear equations, which have exact solutions, linear inequalities define a set of possible solutions. For example, the inequality (2x + 3 < 7) indicates that any value of (x) that satisfies this condition is part of the solution set.
What does it mean to solve a system of quadratic equations?
Solving a system of quadratic equations involves finding the values of the variables that satisfy all equations in the system simultaneously. This typically requires identifying the points of intersection between the curves represented by the quadratic equations on a graph. The solutions can be real or complex numbers and may include multiple pairs of values, depending on the nature of the equations. Techniques for solving these systems include substitution, elimination, or graphical methods.
