For what value of k the system of equation has unique solution?

For what value of k the system of equation has unique solution?

Solution. Thus for all real values of k other than 10, the given system of equations will have a unique solution. Hence, the required value of k is 10. There is no value of k for which the given system of equations has an infinite number of solutions.

What is the formula for unique solution?

Condition for Unique Solution to Linear Equations A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. i.e., if the two lines are neither parallel nor coincident.

For what value of k do the equations 3x y +8 0 and 6x Ky represent coincident lines?

Answer: For k = 2, the two equations 3x-y+8=0 and 6x-ky=-16 represent coincident lines. Solution: The given equations are 3x-y+8=0 and 6x-ky+16 = 0.

What is the value of K that will make the given system of linear equation inconsistent?

k=2

What is an example of an inconsistent equation?

Inconsistent equations is defined as two or more equations that are impossible to solve based on using one set of values for the variables. An example of a set of inconsistent equations is x+2=4 and x+2=6.

What is a dependent system of equations?

If the systems of equations are dependent, it means that there are an infinite number of solutions. So in order to determine a single solution (out of the infinite possibilities), the value of x will depend on what you choose as the value of y. That is, x varies with y (and y varies with x).

What are the 3 types of system of equations?

There are three types of systems of linear equations in two variables, and three types of solutions.

• An independent system has exactly one solution pair (x,y). The point where the two lines intersect is the only solution.
• An inconsistent system has no solution.
• A dependent system has infinitely many solutions.

How do I solve system of equations?

Here’s how it goes:

1. Step 1: Solve one of the equations for one of the variables. Let’s solve the first equation for y:
2. Step 2: Substitute that equation into the other equation, and solve for x.
3. Step 3: Substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

What is the solution to the following system of equations 3x 2y?

Answer: Infinite solutions. Therefore, there are infinite solutions to the system of equations.

How do you solve a system of equations with two variables?

Solving Systems of Equations in Two Variables by the Addition Method

1. Write both equations with x– and y-variables on the left side of the equal sign and constants on the right.
2. Write one equation above the other, lining up corresponding variables.
3. Solve the resulting equation for the remaining variable.

How do you eliminate a system of equations?

The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.

What makes a system of equations have infinite solutions?

Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

How do you know if an equation has one solution no solution or infinite solutions?

Explanation: When finding how many solutions an equation has you need to look at the constants and coefficients. The coefficients are the numbers alongside the variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

How do you tell the number of solutions an equation has?

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

How do you know if an equation has 2 solutions?

The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it’s less than 0, there are no solutions. If it’s equal to 0, there is one solution.