Chapter 11, Problem 4CA

To determine

To calculate the system of equation.

Answer to Problem 4CA

  $y=-3x-2$

Explanation of Solution

Given information:

The solution is $(-2,4),(1,-5)$

The system of the equation is,

  $\begin{array}{l}y=\_x+\_\\ y=2x^2-x-6\end{array}$

Formula used:

Equation is line is,

  $y-y_1^{}=m(x-x_1^{})$

Slope is,

  $m=\frac{y_2^{}-y_1^{}}{x_2^{}-x_1^{}}$

Calculation:

For the slope, substituting the values,

  $m=\frac{-5-4}{1-(-2)}$

So,

  $m=\frac{-9}{3}$

On solving,

  $m=-3$

For the equation of line, substituting the values,

  $y-4=-3\{x-(-2)\}$

So,

  $y-4=-3(x+2)$

On solving,

  $y-4=-3x-6$

Shifting the values,

  $y=-3x-6+4$

On solving,

  $y=-3x-2$

Hence, the system of equation is,

  $\begin{array}{l}y=-3x-2\\ y=2x^2-x-6\end{array}$