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What does it mean when a system of two linear equations does not have a solution?
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What does it mean for a system of linear equations to have no solutions?
It means that there is no set of values for the variables such that all the linear equations are simultaneously true.
What does it mean to be a solution to a system of equations?
basically it means an answer for a multiplication problem
What does a single solution to a system of equations mean?
It represents the point of intersection on a graph.
What it means to be a solution to a linear system algebraically?
A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.
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 does it mean for a system of linear equations to have no solutions?
It means that there is no set of values for the variables such that all the linear equations are simultaneously true.
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.
When two line graphs are crossing what does it mean?
It means that the coordinates of the point of intersection satisfy the equations of both lines. In the case of simultaneous [linear] equations, these coordinates are the solution to the equations.
What does it mean to be a solution to a system of equations?
basically it means an answer for a multiplication problem
What does a single solution to a system of equations mean?
It represents the point of intersection on a graph.
What does it mean both algebraically and graphically when an ordered pair is a solution to a system of two linear equations?
If an ordered pair is a solution to a system of linear equations, then algebraically it returns the same values when substituted appropriately into the x and y variables in each equation. For a very basic example: (0,0) satisfies the linear system of equations given by y=x and y=-2x By substituting in x=0 into both equations, the following is obtained: y=(0) and y=-2(0)=0 x=0 returns y=0 for both equations, which satisfies the ordered pair (0,0). This means that if an ordered pair is a solution to a system of equations, the x of that ordered pair returns the same y for all equations in the system. Graphically, this means that all equations in the system intersect at that point. This makes sense because an x value returns the same y value at that ordered pair, meaning all equations would have the same value at the x-coordinate of the ordered pair. The ordered pair specifies an intersection point of the equations.
Do equations with different slopes and different y-intercepts have a solution?
TWO linear equations with different slopes intersect in one point, regardlessof their y-intercepts. That point is the solution of the pair.However, this does not mean that three (or more) equations in two variables, even if they meet the above conditions, have a solution.
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 it means to be a solution to a linear system algebraically?
A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.
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.
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.
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.
