How do you solve the system of linear equations #2x − 3y = 3# and #5x − 4y = 4#?
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There are two methods. 1. solve for one variable and then substitute.
2. Add or subtract the equations so that one variable is eliminated then substitute.
# 2x -3y = 3 # add 3y to both sides
# 2x -3y + 3y = -3y +3# gives
# 2x = +3y +3 # divide both sides by 2
# (2x)/2 = (+3y)/2 + 3/2 # which gives.
# x = +3/2 y + 3/2 # Now substitute into the other equation
# 5x -4y = 4 = 5(+3/2y + 3/2) -4y = 4# which gives
# (+15/2)y + 15/2 -4y = 4# multiply everything by 2
# 2(+15/2)y + 2 (15/2) -4y = 4 #
# +15y -4y + 15 = 4 # subtract 15 from both sides
# 11y + 15 -15 = 4 -15 #
# 11y = - 11 # divide both sides by 11
# (11y/11 = -11/11# gives
# y = -1 #
# 2x -3(-1) = 3#
# 2x + 3 = 3 # subtract 3 from both sides
# 2x + 3 -3 = 3 -3 # so
# 2x = 0# divide both sides by two
# 2x/2 = 0/2 #
# x = 0 #
