Question

the value of k for which the pair of equations Kx-2y=3 and 5x-4y=2 will have infinitely many solutions is? (a) 12/3. (b) -11/2. (c) 11/2 (d) 15/2​

Answer 1

Answer:

In general there may be:

                       n equations

                       v variables

Solving systems of equations

           There are four methods for solving systems of linear equations:

                       a.  graphical solution

                       b.  algebraic solution

                       c.  elimination method

                       d.  substitution method

Graphical solution

Example 1

           given are the two following linear equations:

                       f(x)  =  y  = 1 +  .5x

                       f(x)  =  y  = 11 -  2x

Graph the first equation by finding two data points.  By setting first x and then y equal to zero it is possible to find the y intercept on the vertical axis and the x intercept on the horizontal axis.

           If x = 0, then  f(0)  =  1  + .5(0)  =  1

           If y = 0, then  f(x)  =  0  = 1  +  .5x

                                               -.5x  =  1

                                                    x  =  -2

           The resulting data points are  (0,1)  and  (-2,0)

Graph the second  equation by finding two data points.  By setting first x and then y equal to zero it is possible to find the y intercept on the vertical axis and the x intercept on the horizontal axis.

           If x = 0, then  f(0)  =  11  - 2(0)  =  11

           If y = 0, then  f(x)  =  0  = 11  -  2x

                                               2x  =  11

                                                    x  =  5.5

           The resulting data points are  (0,11)  and  (5.5,0)

At the point of intersection of the two equations x and y have the same values.  From the graph these values can be read as x = 4 and y = 3.

Step-by-step explanation: