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Can a system of two linear equations have only two or three soltions why or why not?
Wiki User
∙ 10y ago
No. There are none, one or infinitely many solutions. No other value is possible.
A system of two linear equation can be represented by two straight lines in space (of 2 or more dimensions).
Such lines can be non-intersecting (0 solutions),
or they can intersect at one point (1 solution),
or they can be coincident (infinitely many solns).
Two non-intersecting lines in 2-d space must be parallel but in spaces of 3 or more dimensions they can simply be non-coplanar. For example, imagine you are in a cuboid room. One line is the join of the walls to your left and behind you, the other line is where the floor meets the far wall. These lines are not parallel but they do not meet.
Wiki User
∙ 10y ago
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What are the three types of system of linear equations?
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.
To solve a three variable system of equations you can use a combination of the elimination and substitution methods?
True. To solve a three variable system of equations you can use a combination of the elimination and substitution methods.
What is of system of equations?
It is essentially a list of equations that have common unknown variables in all of them. For example, a+b-c=3 4a+b+c=1 a-2b-7c=-2 would be a system of equations. If there are the same number of equations and variables you can usually, but not always, find the solutions. Since there are 3 equations and 3 variables (a, b, and c) in this example one can usually find the value of those three variables.
Is y x 5 linear?
No, they are simply three expressions: there is no equation - linear or otherwise.
What are linear equations?
Linear equations are equations whose only terms are constants and/or single variables raised to the first power. More than one variable is allowed in a linear equation, but it is not allowed to be multiplied with another variable. Constants are allowed to be multiplied to variables in linear equations. These equations are called "linear" due to the fact that their solution set forms a line when represented in classic Euclidean space, e.g. when graphed on the mutually perpendicular x, y, and z axes of the Cartesian coordinate system.Here are three examples of linear equations:Slope-intercept form:y = mx + b, where x is the independent variable, y is the dependent variable, and m and b are constants. This representation of a linear equation is useful because the slope of the line formed by its solution set is m.Point-slope form:y - y1 = m(x - x1), where x is the independent variable, y is the dependent variable, and m is the constant slope. The point (x1,y1) is included in this form to explicitly show that the independent distances of x and y between two points are proportional to each other by the proportionality constant, m, the slope.Intercept form:x/a + y/b = 1, where x and y are variables and a and b are non-zero constants. This form is useful because the x and y intercepts, i.e. the points on a graph where this line crosses the x and y axes, are a and b, respectively.
How many solutions does a system of linear equations in three variables have?
1
What are the three types of system of linear equations?
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.
Kinds of system of linear equation in two variables?
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
What are the three kinds of linear equations?
The three types of linear equations are: Consistent Dependent, Consistent Independent, and Inconsistent.
What are the three types of systems of linear equations and their characteristics?
Independence:The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.Consistency:The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as the statement that 0 = 1.Homogeneous:If the linear equations in a given system have a value of zero for all of their constant terms, the system is homogeneous.If one or more of the system's constant terms aren't zero, then the system is nonhomogeneous.
What the system of linear equation in two variabes which has no solution?
For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.) For example y = mx + b and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution. With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.
How do you decide whether to use elimination or subsitution to solve a three-variable system?
There is no simple answer. Sometimes, the nature of one of the equations lends itself to the substitution method but at other times, elimination is better. If they are non-linear equations, and there is an easy substitution then that is the best approach. With linear equations, using the inverse matrix is the fastest method.
What are the uses of linear inequalities?
In question and answer logic answers are given and if they fall in an area bounded by the inequality then it is a good answer. After graphing three or more inequalities the vertexes are the possible maxima of the system of equations.
What is the disadvantage of using the substitution method in solving linear equations rather than the graph method?
There are no disadvantages. There are three main ways to solve linear equations which are: substitution, graphing, and elimination. The method that is most appropriate can be found by looking at the equation.
What are the three types of possible solutions to a system of equations?
If the equations are linear, they may have no common solutions, one common solutions, or infinitely many solutions. Graphically, in the simplest case you have two straight lines; these can be parallel, intersect in a same point, or actually be the same line. If the equations are non-linear, they may have any amount of solutions. For example, two different intersecting ellipses may intersect in up to four points.
What are system of linear equations?
Systems of linear equations are simply two or more linear equations related to each other, whether it be through having similar variables or describing similar processes.Linear equations are equations whose only terms are constants and/or single variables raised to the first power. More than one variable is allowed in a linear equation, but it is not allowed to be multiplied with another variable. Constants are allowed to be multiplied to variables in linear equations. These equations are called "linear" due to the fact that their solution set forms a line when represented in classic Euclidean space, e.g. when graphed on the mutually perpendicular x, y, and z axes of the Cartesian coordinate system.Some examples of linear equations are as follows:x+2 = 3x+y+z = 42*a+3*b+4*c+5*d = 10*eIf these three linear equations were all necessary to describe something mathematically, they would be a system of linear equations.To solve a system of linear equations for every unknown, the number of variables must be less than or equal to the number of equations.To actually solve systems of linear equations, the easiest way is to use a calculator and linear algebra.If you had something like this:{ 2*x+3*y = 5{ 4*x+10*y = 7What you would do is this:1. Put the coefficients in a matrix:[2 3][4 10]2. Now put the answers in a matrix:[5][7]3. Invert the matrix of the coefficients and multiply that by the answer:[2 3] ^(-1) = [1.25 -.375][4 10] [-.5 .25]4. Multiply this by the matrix[5][7][1.25 -.375] * [5][-.5 .25] [7]=[3.625][-0.75]Meaning your x = 3.625 and your y = -.75
To solve a three variable system of equations you can use a combination of the elimination and substitution methods?
True. To solve a three variable system of equations you can use a combination of the elimination and substitution methods.
