Chapter SH, Problem 6.13EP

To determine

To solve system of equation using elimination

  $2x+5y=-8$

  $4x-2y=0$

Answer to Problem 6.13EP

  $y=\frac{-4}{3}$

  $x=\frac{-2}{3}$

Explanation of Solution

Given information:

  $2x+5y=-8$

  $4x-2y=0$

Calculation:

  $2x+5y=-8\mathrm{.......}(1)$

  $4x-2y=0\mathrm{.......}(2)$

Multiply equation (1) by 2

  $2(2x+5y=-8)$

So,

  $4x+10y=-16\mathrm{......}(3)$

Then, subtracting equation (2) from (3)

  $\begin{array}{l}4x+10y=-16\\ -(4x-2y=0)\\ \overline{0+12y=-16}\end{array}$

Then, $12y=-16$

So,

  $y=\frac{-16}{12}$

On solving.

  $y=\frac{-4}{3}$

Substituting value of y in equation (2)

  $4x-2(\frac{-4}{3})=0$

On solving,

  $4x+\frac{8}{3}=0$

On soiving,

  $x=\frac{-2}{3}$