Chapter 7.1, Problem 44E

To determine

To solve the system of equations $x^2-y=3;x-y=1$ and then verify graphically

Answer to Problem 44E

The solution of the system of equations is: $(-1,-2)\text{and}(2,1)$

Explanation of Solution

Given information: The system of equations is: $x^2-y=3;x-y=1$

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

Calculation:

  $x^2-y=3(1)$

  $x-y=1(2)$

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

The eq. (1) becomes as:

  $x^2-x+1=3$

  $x^2-x-2=0$

  $\Rightarrow x^2-2x+x-2=0$

  $\Rightarrow x(x-2)+1(x-2)=0$

  $\Rightarrow (x+1)(x-2)=0$

The points of intersection are: $(-1,-2)\text{and}(2,1)$

The graph of the system of equations is:

  

From the above graph, it can be concluded that the point of intersection is $(-1,-2)\text{and}(2,1)$

Hence the result is verified.