For what values of A and B the following equations have infinite solutions 2x 3y 7 K 1?

Given pair of linear equations is

2x + 3y = 7

2px + py = 28 – qy

or 2px + (p + q)y – 28 = 0

On comparing with ax + by + c = 0,

We get,

Here, a1 = 2, b1 = 3, c1 = – 7;

And a2 = 2p, b2 = (p + q), c2 = – 28;

a1/a2 = 2/2p

b1/b2 = 3/ (p+q)

c1/c2 = ¼

Since, the pair of equations has infinitely many solutions i.e., both lines are coincident.

a1/a2 = b1/b2 = c1/c2

1/p = 3/(p+q) = ¼

Taking first and third parts, we get

p = 4

Again, taking last two parts, we get

3/(p+q) = ¼

p + q = 12

Since p = 4

So, q = 8

Here, we see that the values of p = 4 and q = 8 satisfies all three parts.

Hence, the pair of equations has infinitely many solutions for all values of p = 4 and q = 8.

For what values of A and B the following equations have infinite solutions 2x 3y 7 K 1?

Find the value of k for which each of the following systems of linear equations has an infinite number of solutions: 2x+3y=7, k 1x+k+2y=3k.

Solution

The given system may be written as2x+3y-7=0 (k−1)x+(k+2)y-3k=0The given system of equation is of the forma1x+b1y+c1 = 0a2x+b2y+c2 = 0Where, a1=2,b1=3,c1=−7a2=k,b2=k+2,c2=3kFor unique solution,we havea1a2=b1b2=c1c2 2k−1=3k+2=−7−3k 2k−1=3k+2 and 3k+2=−7−3k ⇒2k+4=3k−3 and 9k=7k+14 ⇒k=7and k=7Therefore, the given system of equations will have infinitely many solutions, if k=7.

For what values of A and B the following equations have infinite solutions 2x 3y 7?

Therefore for infinite number of solutions a=4 and b=8.

How do you know if two equations have infinite solutions?

Conditions for Infinite Solution The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

How do you know if there are an infinite amount of solutions?

Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.