Chapter SH, Problem 9.20EP

To determine

To find: the solution of the system of equation.

Answer to Problem 9.20EP

The equation will be satisfied at $\text{x=}\frac{\text{5±}\sqrt{\text{63}}\text{i}}{\text{2}}$ .

Explanation of Solution

Given:

  $\text{y=-3x+1}$ .

  ${\text{y-x}}^{\text{2}}\text{=23-8x}$ .

Concept used:

Addition and elimination method are used to solve the two unknown variables having two equation.

In additions method the two equation will sum up and eliminating method two equation will subtract.

Substituting one another is also done to solve two unknown variables.

The quadratic formula:

  $\text{x=}\frac{\text{-b±}\sqrt{{\text{b}}^{\text{2}}\text{-4ac}}}{\text{2a}}$ .

Calculation:

  $\text{y=-3x+1}$ ………… $\left(\text{i}\right)$

  ${\text{y-x}}^{\text{2}}\text{=23-8x}$ ……………. $\left(\text{ii}\right)$

Putting value $\text{y}$ from equation $\left(\text{i}\right)$ in $\left(\text{ii}\right)$ :

  $\left(\text{-3x+1}\right){\text{-x}}^{\text{2}}\text{=23-8x}$ .

  ${\text{-3x+1-x}}^{\text{2}}\text{=23-8x}$ .

  $\Rightarrow {\text{x}}^{\text{2}}\text{-5x+22=0}$ .

  $\text{a=1,b=-5 and c=22}$ .

  $\text{x=}\frac{\text{-b±}\sqrt{{\text{b}}^{\text{2}}\text{-4ac}}}{\text{2a}}$ .

  $\Rightarrow \text{x=}\frac{\text{-}\left(-5\right)\text{±}\sqrt{{\left(-5\right)}^{\text{2}}\text{-4}\left(1\right)\left(22\right)}}{\text{2}\left(1\right)}$ .

  $\Rightarrow \text{x=}\frac{\text{5±}\sqrt{-63}}{\text{2}}$ .

  $\text{x=}\frac{\text{5±}\sqrt{\text{63}}\text{i}}{\text{2}}$ .

Hence, at $\text{x=}\frac{\text{5±}\sqrt{\text{63}}\text{i}}{\text{2}}$ the equation satisfied.