The value of k for which the pair of equations and represent coincident lines

The given system of equations may be written as

x + 2y + 7 = 0

2x + ky + 14 = 0

The given system of equations is of the form

`a_1x + b_1y + c_1 = 0`

`a_2x + b_2y + c_2 = 0`

Where `a_1 = 1, b_1 = 2, c_1 = 7`

And `a_2 = 2,b_2 = k, c_2 = 14`

The given equations will represent coincident lines if they have infinitely many solutions,

The condition for which is

`a_1/a_2 = b_1/b_2 = c_1/c_2 =. 1/2 = 2/k = 7/14 => k = 4`

Hence, the given system of equations will represent coincident lines, if  k = 4

Hello, I'm sorry. We need to use the elimination method to solve the problem. I want Elena to eliminate Q if I look at this equation. I have positive and negative questions. I would make these top one and two. When I add these two equations together, I am able to eliminate Quer. If I take this top off and add everything up, I end up with six p and 14. I give to everything in the first equation and the second equation. I'm doing the same thing, so I'm just going to rewrite it. I don't have to modify it. I'm going to add these together six plus two p as thieves cancel out. P is equal to one if I divide it by eight and I get zero and 14 plus negatives. We have to solve the case of the accused. This p is going to be plugged back into the equation. The equations can be used by us. I will use this one because Q has solved it. It's happening. One cube is all. It is a little easier because of that. I'm going to replace in. I'm going to solve it because this P is the same as the one that's here. One is three close Q. Three will be subtracted on both sides. It's equal to four when you end up with Q. You're final answer is the pair of 0.14

Solution : The given system of equations is
2x + 3y = 7
(p + q)x + (2p - q)y = 21
Here `a_(1) = 2, b_(1) = 3`, and `c_(1) = 7`
`a_(2) = p + q, b_(2) = 2p - q` and `c_(2) = 21`
The given system will have infinite number of solutions if
`(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2))`
`(2)/(p + q) = (3)/(2p - q) = (7)/(21)`
Taking first two and last two expressions
`(7)/(p + q) = (1)/(3)` and `(3)/(2p - q) = (1)/(3)`
implies p + q = 6 and 2p - q = 9
Solving p + q = 6 and 2p - q = 9, we get
p = 5 and q = 1
Hence, the given system of equations will have infinitely many solutions, if p = 5 and q = 1.

Find the value of p and q for which the system of equations represent coincident lines 2x +3y = 7, (p+q+1)x +(p+2q+2)y = 4(p+q)+1

Ans: a1  = 2, b1 = 3, c1 = 7

a2  = p + q + 1 , b2 = p + 2q + 2 , c2 = (p + q )+ 1

For the following system of equation the condition must be

a1/a2 = b1/b2 =c1/c2

=> 2/p+q+1 = 3/ p + q +2 =  7 /4(p+q)+1

=>  2/p+q+1 = 7 /4(p+q)+1

7p +14q + 14 = 12p + 12q + 3

= 5p - 2q - 11 = 0    ----------------(2)

p + q + - 5 = 0

5p - 2q - 11 = 0

From (1) and (2)

5p + 5q - 25 = 0

5p - 2q - 11 = 0

Solve it, to get  q = 2

Substitute value of q in equation (1)

p + q - 5 = 0

On solving we get, p = 3 and q = 2

For what values of P and Q will be the following pair of linear equations has infinitely many solutions?

For values of p = -1 and q =2, the pair of linear equations 4x + 5y = 2; (2p + 7q) x + (p + 8q) y = 2q - p + 1 has infinitely many solutions.

For what value P and Q the system of equations 2x 3y 7 and 2px p q y 28 have infinite number of solutions?

2x+ 3y= 7 and 2p + py = 28 – qy, if the pair of equations have infinitely many solutions. Find p and q. Since, the pair of equations has infinitely many solutions i.e., both lines are coincident. Here, we see that the values of p = 4 and q = 8 satisfies all three parts.

For what value of k system of equations has coincident lines?

Hence, the given system of equations will represent coincident lines, if k=4.

What system of linear equations represent coincident lines?

Equation of Coincident Lines: When two lines are coinciding to each other, then there could be no intercept difference between them

The given system of equations may be written as

The given system of equations is of the form

The given equations will represent coincident lines if they have infinitely many solutions,
The conditionfor which is

Hence, the given system of equations will represent coincident lines, if k=4.

For what values of k is the pair of equations?

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