Answer:
A
Step-by-step explanation:
Given the 2 equations
y = x² - 4x + 8 → (1)
y = 2x + 3 → (2)
Since both express y in terms of x we can equate the left sides, that is
x² - 4x + 8 = 2x + 3 ( subtract 2x + 3 from both sides )
x² - 6x + 5 = 0 ← in standard form
(x - 1)(x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 5 = 0 ⇒ x = 5
Substitute these values into (2) for corresponding values of y
x = 1 : y = (2 × 1) + 3 = 2 + 3 = 5 ⇒ (1, 5)
x = 5 : y = (2 × 5) + 3 = 10 + 3 = 13 ⇒ (5, 13)
Solutions are (1, 5) and (5, 13)
Answer:
A. [tex](1,5)[/tex] and [tex](5,13)[/tex]
Step-by-step explanation:
We have been given a system of equations. We are asked to find the solution of our given system.
[tex]\left \{ {{y=x^2-4x+8}\atop {y=2x+3}} \right.[/tex]
Equate both equations:
[tex]x^2-4x+8=2x+3[/tex]
[tex]x^2-4x-2x+8-3=2x-2x+3-3[/tex]
[tex]x^2-6x+5=0[/tex]
Split the middle term:
[tex]x^2-5x-x+5=0[/tex]
[tex]x(x-5)-1(x-5)=0[/tex]
[tex](x-5)(x-1)=0[/tex]
Use zero product property:
[tex](x-5)=0\text{ (or) }(x-1)=0[/tex]
[tex]x=5\text{ (or) }x=1[/tex]
Now, we will substitute both values of x, in our given equation to solve for y.
[tex]y=2x+3[/tex]
[tex]y=2(1)+3[/tex]
[tex]y=2+3[/tex]
[tex]y=5[/tex]
One solution: [tex](1,5)[/tex]
[tex]y=2x+3[/tex]
[tex]y=2(5)+3[/tex]
[tex]y=10+3[/tex]
[tex]y=13[/tex]
2nd solution: [tex](5,13)[/tex]
Therefore, option A is the correct choice.
