How do you find the solution of the system of equations #x+2y=5# and #2x-3y=-4#?

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Answer 1 · 2015-05-21T08:46:12

The answer is #x=5-2y# and #y=2#

Problem: Solve the system of equations #x+2y=5# and #2x-3y=-4#.

First equation. Solve for #x#.

#x+2y=5#

Subtract #2y# from both sides.

#x=5-2y#

Second equation. Solve for #y#.

Substitute #5-2y# for #x# in the other equation. Solve for #y#.

#2x-3y=-4# =

#2(5-2y)-3y=-4#

Distribute the #2#.

#10-4y-3y=-4#

Combine like terms.

#-7y+10=-4# =

#-7y=-14#

Divide both sides by #-7#.

#y=2#

Check your answers by substituting the values for #x# and #y# back into both of the original equations.

#x+2y=5# =

#5-2*2+2*2=5# =

#5-4+4=5# =

#5=5#

#2x-3y=-4# =

#2(5-2*2)-3*2=-4#

Distribute the #2#.

#10-8-6=-4# =

#-4=-4#

The answers check!