Final answer:
To solve the system of equations, set the two equations equal to each other and solve the resulting quadratic equation.
The solutions are x = 2 and x = 4.
Substituting these values back into the original equations, the corresponding values of Y can be found.
Step-by-step explanation:
To solve the system of equations:
Y = x^2 - 4x + 3
Y = 2x - 5
We can set the two equations equal to each other:
x^2 - 4x + 3 = 2x - 5
Combining like terms and setting the equation equal to zero:
x^2 - 6x + 8 = 0
Now we can solve this quadratic equation using factoring, completing the square, or quadratic formula.
If factored, the equation becomes:
(x - 2)(x - 4) = 0
Therefore, the solutions are x = 2 and x = 4.
Substituting these values back into either of the original equations, we can find the corresponding values of Y:
For x = 2:
Y = (2^2) - 4(2) + 3
= -1
For x = 4:
Y = (4^2) - 4(4) + 3
= 7