Chapter 7.1, Problem 35E

To determine

To solve the system of equations $2x^2-y=1;x-y=2$ by the method of substitution and then verify graphically

Answer to Problem 35E

The system of equations has no solution

Explanation of Solution

Given information: The system of equations is: $2x^2-y=1;x-y=2$

Concept used: If the system of equations intersects, the point of intersection is the solution of the equation.

Calculation:

  $2x^2-y=1(1)$

  $x-y=2(2)$

Put the value $y=x-2$ in eq. (1).

The eq. (1) becomes as:

  $2x^2-x+2=1$

  $\Rightarrow 2x^2-x+1=0$

  $\Rightarrow x=\frac{1\pm \sqrt{1-8}}{4}$

  $\Rightarrow x=\frac{1\pm i\sqrt{7}}{4},\text{imaginary}\text{values}\text{of}\text{x}$

These two curves will not intersect.

The graph of the system of equations is:

  

From the above graph, it can be concluded that the two curves will never intersect each other.

Hence the result is verified.