Final answer:
The solution to the given linear quadratic system of equations is found by substituting the expression for Y from the first equation into the second and solving the resulting quadratic equation, which gives us the solutions (-5, -3) and (1, 3).
Step-by-step explanation:
The student asked about the solution of the linear quadratic system of equations given by Y = x²+5x-3 and Y-x = 2. To solve the system, we can use substitution since both equations are solved for Y. We substitute the expression from the first equation into the second one in place of Y. This leads to the equation x²+5x-3-x = 2, which simplifies to x²+4x-5 = 0.
To solve this quadratic equation, we can factor it to obtain (x+5)(x-1) = 0, resulting in the solutions x = -5 and x = 1. We then plug these values back into one of the original equations to find the corresponding Y values. For x = -5, we get Y = -5²+5*(-5)-3 = 25-25-3 = -3. For x = 1, we get Y = 1²+5*1-3 = 1+5-3 = 3.
Therefore, the solutions to the system of equations are (-5, -3) and (1, 3), which means the system has two intersection points.