Hey guys!
When you have two lines intersecting, the point of intersection must satisfy the equation for both lines
At that point, both lines exist and both line equations must be valid at the same time
Always take a quick glance through all the answer choices to see if there's an immediate fit
If you don't see anything, start plugging in the answer choices and see which one works. Start with the simpler ones because, hey you never know
B.
\(y = x\sqrt{3} + \sqrt{2}\)
\(\sqrt{2} = \sqrt{3}(\sqrt{3}) + \sqrt{2} = 3 + \sqrt{2}\)
This is wrong
C. \(\sqrt{3} = \sqrt{2}\sqrt{3} + \sqrt{2}
\)
This is wrong
D. \(\sqrt{3} + \sqrt{2} = (1)\sqrt{3} + \sqrt{2}\)
This one works! Let's try it for the other line
\(
y = x\sqrt{2} + \sqrt{3}\)
\(\sqrt{3} + \sqrt{2} = (1)\sqrt{2} + \sqrt{3}\)
This one works for both lines! (D) is the correct answer
It can be spotted by seeing that 1 as the x is easy to multiply and check the equations against the y
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