eththomas1951 eththomas1951
  • 21-10-2019
  • Mathematics
contestada

Where do the lines given by y=x+b and y=2x+1 intersect?

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carlos2112
carlos2112 carlos2112
  • 22-10-2019

Answer:

[tex]x=b-1\\y=2b-1[/tex]

Step-by-step explanation:

We have a 2x2 equation system. First, rewrite it like this:

[tex]-2x+y=1\hspace{5}(1)\\-x+y=b\hspace{5}(1)[/tex]

Solving the system using elimination method:

(1)-(2)

[tex]-2x-(-x)+y-y=1-b\\x=b-1\hspace{5}(3)[/tex]

Replacing (3) in (2)

[tex]-(b-1)+y=b\\[/tex]

Adding (b-1) to both sides:

[tex]y=b+(b-1)=b+b-1=2b-1[/tex]

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