How do you solve the system of linear equations #2x − 3y = 3# and #5x − 4y = 4#?

1 Answer

Answer:

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.

Explanation:

# 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 #