Ideal answer for – is a linear equation solvable?

Yes, a linear equation is solvable by finding the value of the unknown variable that satisfies the equation.

Further information is provided below

Linear equations are fundamental to mathematics and are used in various fields like science, engineering, and economics. A linear equation is a polynomial equation of degree one, meaning it has no exponent other than the first power. A linear equation can be written in the form of y = mx + b or ax + by = c, where m, b, a, b, and c are constants. The primary goal of solving linear equations is to find the value of the unknown variable that satisfies the equation.

According to famous mathematician Euclid, “The laws of nature are but the mathematical thoughts of God.” Linear equations are an essential tool for understanding the laws of nature, particularly in the field of physics and engineering.

Here are some interesting facts about linear equations:

  • The concept of linear equations has been around since ancient Egyptian and Babylonian times.
  • Linear equations were first systematically studied by the ancient Greek mathematicians, including Euclid, who wrote the first known book on linear algebra, the “Elements.”
  • Linear equations are used in almost every aspect of modern life, including computer graphics, financial analysis, and even weather forecasting.
  • The solution to a linear equation can be represented graphically as the point where the line intersects the y-axis.
  • If a linear equation has only one variable, then it is called a linear function.

Here is a table showing some examples of linear equations:

Equation Solution
2x + 3 = 7 x = 2
5y – 10 = 0 y = 2
3x – 2y = 12 x = 4,y = 3

In conclusion, linear equations are solvable, and finding their solution can help us understand the laws of nature and everyday life better. The ability to solve linear equations is crucial in various fields of study and is a fundamental aspect of mathematical problem-solving. As Albert Einstein said, “Pure mathematics is, in its way, the poetry of logical ideas.”

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See the answer to “Is a linear equation solvable?” in this video

The video discusses the concept of a system of linear equations being unsolvable and how it can occur in situations where not all necessary information is provided. A specific example of calculating the lengths of five highways is used to show how the lack of solvability can lead to infinitely many solutions or no solutions at all. The importance of ensuring solvability to determine all necessary values is emphasized.

See more possible solutions

The system of linear interval equations Ax = b is said to be solvable if each system Ax = b with A ∈ A, b ∈ b has a solution.

A linear equation system is not solvable if it is inconsistent, i.e. if it has no solutions. The Kronecker-Capelli criterion can be used to determine if a system of equations is solvable. The system of equations is solvable if and only if the rank of the system matrix is equal to the rank of the augmented matrix. If the rank of the system matrix is not equal to the rank of the augmented matrix, then there can be no solution. Another way to tell if a linear system in two variables has no solution is to solve the system and get a nonsense equation, or to look at the graph and see if the two lines are parallel.

Yes: by showing that the system is equivalent to one in which the equation 0 = 3 0 = 3 must hold, you have shown the original system has no solutions. By definition, a system of linear equation is said to be "consistent" if and only if it has at least one solution; and it is "inconsistent" if and only if it has no solutions.

Using the Kronecker-Capelli criterion, the system of equations is solvable if and only if the rank of the system matrix is equal to the rank of the augmented matrix. The rank of the system matrix is clearly 2 2 and of the augmented matrix is 3 3. Therefore, there can be no solution.

There are a few ways to tell when a linear system in two variables has no solution: Solve the system – if you solve the system and get a nonsense equation (such as 0 = 1), then there is no solution. Look at the graph – if the two lines are parallel (they never touch), then there is no solution to the system.

• Yes: by showing that the system is equivalent to one in which the equation 0=3 must hold, you have shown the original system has no solutions.
• By definition, a system of linear equation is said to be “consistent” if and only if it has at least one solution; and it is “inconsistent” if and only if it has no solutions. So “showing a system of linear equations is not solvable” (has no solutions) is, by definition, the same thing as showing that the system of linear equations is “inconsistent”.
• “A system doesn’t have a unique solution” can happen in two ways: it can have more than one solution (in which case it has infinitely many solutions), or it can have no solutions. Only in the second case do we say the system is “inconsistent”.
• One of the easiest ways to find solutions of systems of linear equations (or show no solutions exist) is Gauss (or Gauss-Jordan) Row Reduction; it amounts to doing the kind of things you did, but in a systematic, algorithmic, recipe-like manner. You ca…

In addition, people ask

Can a linear equation be solved?

To solve linear equations, find the value of the variable that makes the equation true. Use the inverse of the number that multiplies the variable, and multiply or divide both sides by it. Simplify the result to get the variable value. Check your answer by plugging it back into the equation.

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How do you know if an equation is unsolvable?

As an answer to this: When you have an equal number of equations and unknowns, put the coefficients on the variables into a matrix and take the determinant of the matrix. If the determinant does NOT equal zero, the system is solvable. If it DOES equal zero, it is not uniquely solvable.

What is an unsolvable system of linear equations?

The reply will be: An underdetermined linear system has either no solution or infinitely many solutions. For example, is consistent and has an infinitude of solutions, such as (x, y, z) = (1, −2, 2), (2, −3, 2), and (3, −4, 2).

How many ways can a linear equation be solved?

As an answer to this: There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method.

Is a system of linear equations solvable?

As an answer to this: So "showing a system of linear equations isnot solvable" (has no solutions) is, by definition, the same thing as showing that the system of linear equations is "inconsistent".

What is a unique solution of a linear equation?

Answer to this: The solution of a linear equation refers to the numerical value which, when substituted for the variable, satisfies the equation. The solution of linear equations can be unique, infinite, or no solution. For linear equations in one variable, there exists only one value that satisfies the equation. Hence, such equations always have unique solutions.

How do you solve a nontrivial linear system?

The response is: However, a linear system is commonly considered as having at least two equations. The simplest kind of nontrivial linear system involves two equations and two variables: One method for solving such a system is as follows. First, solve the top equation for in terms of : Now substitute this expression for x into the bottom equation:

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How do you know if two linear systems are equivalent?

Answer to this: Two linear systems using the same set of variables are equivalent if each of the equations in the second system can be derived algebraically from the equations in the first system, and vice versa. Two systems are equivalent if either both are inconsistent or each equation of each of them is a linear combination of the equations of the other one.

Is a system of linear equations solvable?

So "showing a system of linear equations isnot solvable" (has no solutions) is, by definition, the same thing as showing that the system of linear equations is "inconsistent".

How to solve linear equations?

Answer: Therefore, by solving linear equations, we get the value of x = 3 and y = 5. Another method for solving linear equations is by using the graph. When we are given a system of linear equations, we graph both the equations by finding values for ‘y’ for different values of ‘x’ in the coordinate system.

How do you solve a nontrivial linear system?

The answer is: However, a linear system is commonly considered as having at least two equations. The simplest kind of nontrivial linear system involves two equations and two variables: One method for solving such a system is as follows. First, solve the top equation for in terms of : Now substitute this expression for x into the bottom equation:

What is the solvability of simultaneous linear equations in two variables?

Now see when the solvability of simultaneous linear equations in two variables (i), (ii) are solavble. (I) If (a₁b₂ – a₂b₁) ≠ 0 for any values of (b₁c₂ – b₂c₁), (a₂c₁ – a₁c₂) we will get the unique solutions for the x and y variables. Therefore, when (a₁b₂ – a₂b₁) ≠ 0, then the system of linear equations are always consistent.

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