Answered

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What is the solution(s) to the system of equations y = x² +4 and y = 2x + 4

Sagot :

loneguy

Answer:

[tex](x,y) = (0,4)~ \text{and}~ (x,y) = (2,8)[/tex]

Step by step explanation:

[tex]y = x^2 +4~~~~~~~~~...(i)\\\\y = 2x +4~~~~~~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~~x^2 +4 = 2x+4\\\\\implies x^2 = 2x\\\\\implies x^2 -2x = 0\\\\\implies x(x-2) = 0\\\\\implies x =0,~ x = 2[/tex]

[tex]\text{Substitute x = 0 in eq (i):}\\\\y = 0^2 +4 = 4\\\\\text{Substitute x = 2 in eq (i):}\\\\y=2^2+4 = 4+4 = 8\\\\\text{Hence,}~ (x,y)= \{(2,8), (0,4)\}[/tex]

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