Chapter SH, Problem 6.1EP

To determine

To solve system of equation

  $y=2x+2$

  $y=-2x-2.$

Answer to Problem 6.1EP

The system of equation is consistent and independent.

Explanation of Solution

Given information:

  $y=2x+2$

  $y=-2x-2.$

Calculation:

  $y=2x+2\mathrm{.........}(1)$

  $y=-2x-2\mathrm{.........}(2)$

Rearrange equations

  $2x-y+2=0\mathrm{.........}(3)$

  $2x+y+2=0\mathrm{.........}(4)$

Compare equation (3) and (4) with $ax+by+c=0$

  $a_1=2$

  $b_1=-1$

  $c_1=2$

  $a_2=2$

  $b_2=1$

  $c_2=2$

Ratios

  $\frac{a_1}{a_2}=\frac{2}{2}=1$

  $\frac{b_1}{b_2}=\frac{-1}{1}=-1$

  $\frac{c_1}{c_2}=\frac{2}{2}=1$

From ratios

  $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}=\frac{c_1}{c_2}$

If $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

System of equation having one solution.

Then, the system of equation is consistent and independent.