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 as
2x+3y-7=0
[k−1]x+[k+2]y-3k=0
The given system of equation is of the form
a1x+b1y+c1 = 0
a2x+b2y+c2 = 0
Where, a1=2,b1=3,c1=−7
a2=k,b2=k+2,c2=3k
For unique solution,we have
a1a2=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=7
Therefore, the given system of equations will have infinitely many solutions, if k=7.
For what value of k will the following equations have infinite solutions 2x 3y 7?
Therefore, the given system of equations will have infinitely many solutions, if k=7.
For what value of K will have infinitely many solutions?
Hence, the given system of equations will have infinitely many solutions, if k=2.
For what value of k will the following equations have infinitely many solutions KX 3y
For what values of k will the following pair of linear equations have infinitely many solutions? kx + 3y - [k – 3] = 0. 12x + ky - k = 0. The value of k which satisfies both the equations is 6.
How do you know if there are infinitely many solutions to an equation?
Well, there is a simple way to know if your solution is infinite. An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If you simplify the equation using an infinite solutions formula or method, you'll get both sides equal, hence, it is an infinite solution.