Final answer:
The solution to a linear quadratic system of equations is found using the substitution method, where one of the equations is solved for one variable and then substituted into the other equation.
Step-by-step explanation:
The student asked about the solution to a linear quadratic system of equations:
- y = x² + 5x - 3
- y - x = 2
To solve this system, we can use the substitution method. Firstly, we isolate y in the second equation:
y = x + 2
We then substitute this expression for y into the first equation:
x + 2 = x² + 5x - 3
Next, we rearrange the equation to form a quadratic equation:
x² + 5x - 3 - x - 2 = 0
x² + 4x - 5 = 0
Now, we need to find the roots of the quadratic equation, which can be solved by factoring, completing the square, or using the quadratic formula. Once we find the x-values, we can substitute them back into y = x + 2 to find the corresponding y-values, giving us the solution(s) to the system.