0
By the substitution method
By the elimination method
By plotting them on a graph
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Describe a consistent independent system of linear equations?
The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.
What does a air of linear equations having a unique solution represent graphically?
Presumably the question concerned a PAIR of linear equations! The answer is two straight lines intersecting at the point whose coordinates are the unique solution.
Does every pair of linear simultaneous equations have a unique solution?
So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.
What is a solution to a system?
an ordered pair that makes both equations true
When is it possible for an ordered pair to be the solution of more than one equation?
Always. Every ordered pair is the solution to infinitely many equations.
What is the solution of a system of linear equations in two variables?
The solution of a system of linear equations is a pair of values that make both of the equations true.
Describe a consistent independent system of linear equations?
The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.
What does a air of linear equations having a unique solution represent graphically?
Presumably the question concerned a PAIR of linear equations! The answer is two straight lines intersecting at the point whose coordinates are the unique solution.
How is a system of 2 linear equations have no solution?
The pair of equations: x + y = 1 and x + y = 3 have no solution. If any ordered pair (x,y) satisfies the first equation it cannot satisfy the second, and conversely. The two equations are said to be inconsistent.
What is the solution of the system of linear equations x equals 5 y equals -2?
7
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.
Does every pair of linear simultaneous equations have a solution?
Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.
Does every pair of linear simultaneous equations have a unique solution?
So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.
How can you determine if the given ordered pair is a solution to the system of equations?
Plug your ordered pair into both of your equations to see if you get they work.
Why are linear equations called linear?
It deals with lines on a graph, part of an ordered pair ,a steady increase in resultant answer
What is an ordered pair that makes all equations in a system true?
That would be the "solution" to the set of equations.
What is a solution to a system?
an ordered pair that makes both equations true
