Question

Solve the system using algebraic methods.

Y=x^2-4x+3
Y=2x-5

Answer 1

To solve the given system of equations, set the two equations equal to each other and solve for x.

The system has two solutions: x = 2 and x = 4.

Step-by-step explanation:

To solve the given system of equations:

Y = x^2 - 4x + 3 (Equation 1)

Y = 2x - 5 (Equation 2)

We can set the two equations equal to each other:

x^2 - 4x + 3 = 2x - 5

Combining like terms:

x^2 - 6x + 8 = 0

We can then solve this quadratic equation using factoring or the quadratic formula:

Solving by factoring:

1. Split -6x into -2x and -4x:
2. x^2 - 2x - 4x + 8 = 0
3. Factor by grouping:
4. x(x - 2) - 4(x - 2) = 0
5. (x - 2)(x - 4) = 0

Setting each factor equal to zero and solving for x:

1. x - 2 = 0
2. x = 2
3. x - 4 = 0
4. x = 4

Therefore, the system has two solutions: x = 2 and x = 4.

Substituting these values back into either Equation 1 or Equation 2 will give the corresponding y-values.