Answer:
(0, 3) and (3, 0)
Step-by-step explanation:
The question asks us to find the solutions to the following system of equations:
[tex]y = x^2 - 4x + 3[/tex]
[tex]y = -x + 3[/tex]
Therefore, as [tex]y = y[/tex], we can say:
[tex]x^2 - 4x + 3 = -x + 3[/tex],
and then solve for [tex]x[/tex]:
⇒ [tex]x^2 - 4x + 3 + x = 3[/tex] [Adding x to both sides of the equation]
⇒ [tex]x^2 - 3x + 3 - 3 = 0[/tex] [Subtracting 3 from both sides]
⇒[tex]x^2 -3x = 0[/tex]
⇒ [tex]x(x-3) = 0[/tex] [Factoring x out]
• [tex]x= \bf 0[/tex] or
• [tex]x- 3 = 0[/tex]
⇒ [tex]x = \bf 3[/tex]
Now we can simply substitute the calculated values of x into any of the given equations to find the respective values of y.
Substituting into the equation [tex]y = -x + 3[/tex] :
• when [tex]x = 0[/tex] ⇒ [tex]y = -(0) +3 = \bf 3[/tex]
• when [tex]x = 3[/tex] ⇒ [tex]y = -(3) + 3 = \bf 0[/tex]
Therefore, the solutions to the given set of equations are (0, 3) and (3, 0).
Learn more about systems of equations here:
https://brainly.com/question/13157348
Learn more about the "zero-product property" that was used to calculate the second value of x here:
https://brainly.com/question/27751281
