How do you solve the following system of equations algebraically: 3x + 2y = 4, 4x + 3y = 7?

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Answer 1 · 2016-11-17T08:51:38

Substitute one equation into the other to give #x=-2#, and #y=5#

You have two equations in two unknowns, #x# and #y#, so this system is potentially solvable exactly.

#3x+2y=4# #(i)#

#4x+3y=7# #(ii)#

From #(i)#, #x=(4-2y)/3#, so substitute this value into #(ii)#:

#4((4-2y)/3)+3y=7#

#16/3-(8y)/3+3y=7#; multiply thru by #3#:

#16-8y+9y=21#

#y=21-16=5#

And substitute this value back into #(i)#:

#3x+2(5)=4#, #x=-2#

If we recheck the original equations, these values are correct.