Chapter ISG, Problem 9.7STP

To determine

To find solution of system of equation algebraically.

Answer to Problem 9.7STP

No real solution

Explanation of Solution

Given information:

  $y=-2x^2+5x+1$

  $y=3x+19$

Calculation:

  $y=-2x^2+5x+\mathrm{1.......}(1)$

  $y=3x+\mathrm{19...............}(2)$

put value of y from equation(2) in (1)

  $3x+19=-2x^2+5x+1$

On solving,

  $0=-2x^2+5x+1-3x-19$

On solving,

  $0=-2x^2+2x-18$

On solving,

  $x^2-x+9=0$

On solving,

  $x^2-x+9=0$

  $a=1$

  $b=-1$

  $c=9$

On solving,

  $x=\frac{-(-1)\pm \sqrt{{(-1)}^2-4(1)(9)}}{2(1)}$

On solving,

  $x=\frac{1\pm \sqrt{1-36}}{2}$

On solving,

  $x=\frac{1\pm \sqrt{-35}}{2}$

The expression is undefined in the set of real numbers

  $x\cancel{\in }ℝ$

No real solution