Chapter 9.9, Problem 12OE

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.

  $7x-y+4z=3$

  $-2x+3y-z=5$

Answer to Problem 12OE

The new equation is $19y+7z=-41$ and the new co-efficient of y is $19$

Explanation of Solution

Given:

  $7x-y+4z=3$

  $-2x+3y-z=5$

Calculation:

Given:

  $7x-y+4z=3$

  $-2x+3y-z=5$

Multiplying equation $7x-y+4z=3$ by - $2$ , we have:

  $-14x+2y-8z=-6$

Multiplying equation $-2x+3y-z=5$ by $7$ , we have:

  $-14x+21y-7z=35$

Subtracting the equation $-14x+21y-7z=35$ from $-14x+2y-8z=-6$ , we have:

  $\begin{array}{l}0x-19y-7z=-41\\ 19y+7z=-41\end{array}$

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

  $19y+7z=-41$

And the new co-efficient of y is $19$ .

Conclusion:

  $19y+7z=-41$

The new co-efficient of y is $19$ .