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When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..

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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Q: When will be the linear equations a1x plus b1y plus c1 equals 0 and a2x plus b2y plus c2 equals 0 has unique solution?
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How do you write linear equations?

Linear equations take the form y= mx+b wherem is the slope [rise(y)/run(x) on a graph]x is the x-value any point on the graphy is the y-value of any point on the graphb is the y-intercept on the graphLinear equations take the form a1x1 + a2x2 + a3x3 + ... + anxn + an+1 = 0Each ai represents a constant, xi a variable.The equation above is linear in n dimensions. In two dimensions, linear equations are typically written ax + by = c. In three dimensions, ax + by + cz = d. After that, the form given above (with the subscripts) is preferred.Any system of n equations and n unknowns may have a unique solution. If two of the equations are multiples of each other, the solution set will not be unique, but represent a line, plane, or subspace. It is also possible the system may have no solution, such as the following:5x + 10y = 55x + 10y = 20This system represents two parallel lines--there is no solution.

When you formulate a system of equations you have at least how many factors?

You don't need ANY factor. To find a unique solution, or a few, you would usually need to have as many equations as you have variables.

Steps in solving problems involving systems of linear equations?

The answer depends on the level of your knowledge. The High level, simple answer is first. The Low level slog follows:HIGH LEVEL, SIMPLESuppose you have n equations of the forma11x1 + a12x2 + ... + a1nxn = bn wherethe as are coefficients,x1, x2, ... xn are the unknown variablesandb1, b2, ... bn are the constants.Write the n linear equations in n unknowns in the form Ax= bwhereA is an n*n matrix of coefficientsx is the n*1 matrix of the unknown variablesandb is the n*1 matrix of the constants.Find the inverse of A.Then x = A-1b.The above method works if the system has a unique solution. If the n equations are not independent, you will need to use a generalised inverse and that starts to get rather complicated. If they are inconsistent, then neither the inverse nor generalised inverse will be found.LOW LEVEL SLOGUse the first equation to express x1 in terms of the other variables. Substitute this value for x1 in the remaining n-1 equations. You now have n-1 equations in n-1 unknown variables.Use the first of the new equations to express x2 in terms of the other variables. Substitute in remaining equations. You now have n-2 equations in n-2 unknown variables.Continue until you have 1 equation in 1 unknown.That will be of the form pxn = q so that xn = q/p.Substitute this value into one of the equations at the 2-equations-in-2-unknowns stage. That will give you xn-1.Work your way back to the top.The two methods are equivalent. There are shortcuts available for matrix inversion (eg using determinants), but these are too complicated to go into here.

What is the definition of the unique number in math?

unique number: The number 1 has only one factor. (It is therefore unique.)

How many circles can be drawn from three non-collinear points?

The answer is 1.Here is the theorem:There is a unique circle passing through points P1 , P2 , P3 if and only if these three points are non-collinear.The proof is not too hard, but involves some linear algebra. I will post a link to it.

Related questions

How is Cramers Rule used in life?

It is used for solving a system of linear equations where the number of equations equals the number of variables - and it is known that there is a unique solution.

When does a system of linear equations in two variables have a unique or one solution?

simultaneous equations

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.

What is a unique solution in linear equations?

This is the case when there is only one set of values for each of the variables that satisfies the system of linear equations. It requires the matrix of coefficients. A to be invertible. If the system of equations is y = Ax then the unique solution is x = A-1y.

What is cramer rule?

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.

What are the applications of cramer's rule?

Cramer's rule is applied to obtain the solution when a system of n linear equations in n variables has a unique solution.

What is the condition for unique solution of linear equation?

The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2.

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.

It is impossible for a system of two linear equations to have exactly one solution. True or False?

False, think of each linear equation as the graph of the line. Then the unique solution (one solution) would be the intersection of the two lines.

Why are systems of equations important?

A single equation is several unknowns will rarely have a unique solution. A system of n equations in n unknown variables may have a unique solution.

How many solutions does x equals 8have?

A solution to an linear equation cx + d = f is in the form x = a for some a, we call a the solution (a might not be unique). Rewrite your sentence: x = 8, 8 is unique. So how many solution does it have?

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.

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