In Example 1, change the sign before y in the first equation from − to + and then solve the system.

Data from Example 1

By substitution, solve the system of equations

We solve the first equation for y, obtaining y = 2x − 4. We now substitute 2x − 4 for y in the second equation, getting x² − (2x − 4)² = 4.

When simplified, this gives a quadratic equation.

We now find the corresponding values of y by substituting into y = 2x − 4. Thus, we have the solutions x = 10/3, y = 8/3, and x = 2, y = 0. As a check, we find that these values also satisfy the equation x² − y² = 4. Compare these solutions with those that would be obtained from Fig. 14.9.

2x - y = 4 x - y = 4