Question #1622e

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Answer 1 · 2018-02-14T18:13:42

#x = 7# and #y = 6#

If you like point form, it is: #(7,6)#

Given:

#2x+y=20" [1]"#
#6x-5y=12" [2]"#

We can use equation [1] to write y in terms of x by subtracting 2x from both sides:

#y=20-2x" [1.1]"#
#6x-5y=12" [2]"#

Substitute the right side of equation [1.1] for y in equation [2]:

#6x-5(20-2x)=12" [2.1]"#

Solve for the value of x:

#6x-100+10x=12" [2.1]"#

#16x = 112#

#x = 7#

We can use either equation [1] or [2] to find the corresponding value of y; I shall use equation [1]:

#2(7)+y = 20#

#y = 6#

Verify that the point #(7,6)# satisfies both equations:

#2(7)+6=20#
#6(7)-5(6)=12#

#20 = 20#
#12=12#

Verified