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Solve the system using algebraic methods

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

User Nluk
by
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1 Answer

4 votes

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

User Troy Hunt
by
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