What is the point of intersection of the lines with equations #x-2y=5# and #2x-5y=-11#?

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Answer 1 · 2016-08-22T15:11:24

#{47, 21}# is the point of intersection.

I'll solve this problem using elimination. You could also use substitution, but I think it's important to familiarize yourself with elimination.

#x - 2y = 5#
#2x - 5y = -11#

#-2(x - 2y) = 5(-2)#
+# (2x - 5y = -11)#

#-2x + 4y = -10#
+#2x - 5y = -11#

We will now add the two equations, in order to cancel out one of the variables, #x# in this case.

#0x - 1y = -21#

#y = 21#

We can now substitute do find #x#.

#x - 2y = 5#

#x - 2(21) = 5#

#x = 5 + 42#

#x = 47#

Hence, our solution point is #(47, 21)#.

Hopefully this helps!