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 $2x+2y+2=0$ Show
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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}\ 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}\ $\Rightarrow p\ The value of $p$ is not equal to $4$. In other words $p$ can take any value other than $4$.
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 4For 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 =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 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.
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