Final answer:
To solve the given linear quadratic system of equations, substitute the linear equation into the quadratic equation, solve for x, and then find the corresponding y values.
Step-by-step explanation:
The solution of the linear quadratic system of equations is found by substituting the linear equation into the quadratic equation or vice versa and solving for the variable. The system in question is:
- y = x^2 + 5x - 3
- y - x = 2
To solve, first express the second equation as y = x + 2. Then substitute this expression for y in the first equation:
x^2 + 5x - 3 = x + 2
Then solve for x:
x^2 + 4x - 5 = 0
This is a quadratic equation, which can be factored or solved using the quadratic formula. After finding x, substitute it back into either the original linear or quadratic equation to find the corresponding y value(s), completing the solution of the system.