Unique solution formula

For which value of p does the pair of equation 4x PY 8 0 and 2x 2y 2 0 has unique solution?

Given: $4x+py+8=0$ and $2x+2y+2=0$

Nội dung chính

For unique solutiona1 / a2≠b1 / b2Therefore.....4 / 2≠p / 2Cross Multiplying....p≠ 4therefore......p can be equal to any value except 4
For which value of p does the pair of equation 4x PY 8 0 and 2x 2y 2 0 has unique solution?
For what value P the following pair of equations has a unique solution 2x py =
What is the formula of unique solution?
Do the equations 4x 3y 1/5 and 12x 9y 18 represent a pair of coincident lines justify?

To do: To find the value of $p$ if the pair of equations has a unique solution.

Solution:

Two equations, 4x+py+8=0 and 2x+2y+2=0

As known the condition for a unique solution is :

$\frac{a_1}{a_2}\
eq\frac{b_1}{b_2}$

Here, $a_1 = 4,\ b_1 = p,\ c_1 = 8$ and $a_2 = 2,\ b_2 = 2$ and $c_2 = 2$

Putting the values in above condition we get:

$\frac{4}{2}\
eq\frac{p}{2}$

$\Rightarrow p\
eq4$

The value of $p$ is not equal to $4$. In other words $p$ can take any value other than $4$.

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For which value of p does the pair of equation given below has unique solution? 4 x+p y+8=02 x+2 y+2=0

Solution

For unique solutiona1 / a2≠b1 / b2Therefore.....4 / 2≠p / 2Cross Multiplying....p≠ 4therefore......p can be equal to any value except 4

For which value of p does the pair of equation 4x PY 8 0 and 2x 2y 2 0 has unique solution?

Hence the given pair of equation has unique solution for all values of p except 4.

For what value P the following pair of equations has a unique solution 2x py =

Therefore, we can say that if $2x + py = - 5$ and $3x + 3y = - 6$ has a unique solution, then $p \ne 2$. In other words, we can say that the given system has a unique solution only if $p \ne 2$. If $p = 2$ then the system has either infinite solutions or no solution.

What is the formula of 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.

Do the equations 4x 3y 1/5 and 12x 9y 18 represent a pair of coincident lines justify?

Therefore, the given equations do not represent a pair of coincident lines.

For what value of p the pair of linear equations has unique solution?

Therefore, the given system will have unique solution for all real values of p other than 4.

For what value P the following pair of equations has a unique solution 2x py =

What is the condition for unique solution?

In a set of linear simultaneous equations, a unique solution exists if and only if, [a] the number of unknowns and the number of equations are equal, [b] all equations are consistent, and [c] there is no linear dependence between any two or more equations, that is, all equations are independent.

For what value of P will have infinitely many solutions?

Answer: p = 6 will make the given pair of linear equations have infinitely many solutions.

For unique solutiona1 / a2≠b1 / b2Therefore.....4 / 2≠p / 2Cross Multiplying....p≠ 4therefore......p can be equal to any value except 4

For which value of p does the pair of equation 4x PY 8 0 and 2x 2y 2 0 has unique solution?

For what value P the following pair of equations has a unique solution 2x py =

What is the formula of unique solution?

Do the equations 4x 3y 1/5 and 12x 9y 18 represent a pair of coincident lines justify?

For what value of p the pair of linear equations has unique solution?

For what value P the following pair of equations has a unique solution 2x py =

What is the condition for unique solution?

For what value of P will have infinitely many solutions?

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