Chapter 9.9, Problem 11OE

To determine

To combine the given equations to obtain an equation in which the co-efficient of x is $0$ and to determine the new co-efficient of y.

  $3x+y-2z=6$

  $2x+2y+z=4$

Answer to Problem 11OE

The new equation is $4y+7z=0$ and the new co-efficient of y is $4$

Explanation of Solution

Given:

  $3x+y-2z=6$

  $2x+2y+z=4$

Calculation:

Given:

  $3x+y-2z=6$

  $2x+2y+z=4$

Multiplying equation $3x+y-2z=6$ by $2$ , we have:

  $6x+2y-4z=12$

Multiplying equation $2x+2y+z=4$ by $3$ , we have:

  $6x+6y+3z=12$

Solving the equation $6x+2y-4z=12$ and $6x+6y+3z=12$ , we have:

  $-4y-7z=0$

  $4y+7z=0$

Thus, the new equation with $0$ co-efficient of x is:

  $4y+7z=0$

And the new co-efficient of y is $4$ .

Conclusion:

  $4y+7z=0$

The new co-efficient of y is $4$ .