Chapter 5, Problem 5CT

To determine

To solve: Solve the system of linear equation using any method. Explain why you chose the method.

  $6x-4y=9$

  $9x-6y=15$

Answer to Problem 5CT

There is no solution for the given system of equations.

In the system of equations we can see that by multiplying equation $\left(i\right)$ by 3 and equation $\left(ii\right)$ by 2 we get the same coefficients across the both equations and then we can eliminate the variables easily.

Explanation of Solution

Given information: The system of given equation is

Calculation: We use the method of elimination to solve

  $6x-4y=\mathrm{9...}\left(i\right)$

  $9x-6y=\mathrm{15...}\left(ii\right)$

multiply equation $\left(i\right)$ by 3 and equation $\left(ii\right)$ by 2, we get

  $18x-12y=\mathrm{27...}\left(iii\right)$

  $18x-12y=\mathrm{30...}\left(iv\right)$

from $\left(iii\right)\&\left(iv\right)$ we can see that left hand side of both equations are same, so we can equate the right hand sides of both the above equations.

we get ,

  $27=30$

which is not true, $27\ne 30$

Hence there is no solution for the given system of equations

In the system of equations we can see that by multiplying equation $\left(i\right)$ by 3 and equation $\left(ii\right)$ by 2 we get the same coefficients across the both equations and then we can eliminate the variables easily.