0
Still curious? Ask our experts.
Chat with our AI personalities
Professor
Devin
BlakeAdd your answer:
Earn +20 pts
What is a solution to a system of equations graphically?
Graphically, it is the point of intersection where the lines (in a linear system) intersect. If you have 2 equations and two unknowns, then you have a 2 lines in a plane. The (x,y) coordinates of the point where the 2 lines intersect represent the values which satisfies both equations. If there are 3 equations and 3 unknowns, then you have lines in 3 dimensional space. If all 3 lines intersect at a point then there is a solution to the system. With more than 3 variables, it is difficult to visualize more dimensions, though.
What is Simultaneous Equations?
Simultaneous equation is nothing: it cannot exist.A system of simultaneous equations is a set of 2 or more equations with a number of variables. A solution to the system is a set of values for the variables such that when the variables are replaced by these values, each one of the equations is true.The equations may be linear or of any mathematical form. There may by none, one or more - including infinitely many - solutions to a system of simultaneous equations.
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.
How many solutions does an independent system of equations have?
It depends. Partly on the domain over which your system of equations is defined - are they integer solutions? Reals or complex numbers? Are the equations linear or more complicated?In any case, there can be none, one or many - including infinitely many.If the system is inconsistent ega + b = 3a + b = 2then there are no solutions.If the system is incomplete (the relevant matrix is singular), you have an infinite number:a + b + c = 1a + 2b + 3c = 2has an infinite number of solutions.A set of n independent linear equations in n unknowns will have a unique solution.A single equation such as (a-2)2 + (b-3)2 + (c-7.5)2 = 0has a unique real-number solution since each on the brackets MUST be zero.
Does this system of equations have one solution no solutions or an infinite number of solutions x - 2y equals -6 and x-2y equals 2?
x - 2y = -6 x - 2y = 2 subtract the 2nd equation from the 1st equation 0 = -8 false Therefore, the system of the equations has no solution.
