How do you solve the system of equations #3x-3y=-9# and #3x-5y=-29# by combining the equations?

1 Answer

Answer:

The easiest way to solve these equations is to subtract the two equations, this eliminating one of the variables ( #x#) and then solving for the other variable (#y#)

#x=7 and y =10#

Explanation:

# + 3x -( + 3x) = 0# so if the two equations are subtracted, the #x# term disappears.

#" "3x - 3y = -9#
#-3x - (-5y) = -( - 29)" "# This gives:

#0x + 2y = + 20" "# next solve for y by dividing both sides by 2

# (2y)/2 = 20/2" "# This gives :

# y = 10#

Next substitute #y =10 #into either of the equation and solve for #x#.

# 3x + (-3 )xx 10 = -9 # This gives

# 3x -30 = -9 " "# Add 30 to both sides giving

# 3x - 30 +30 = -9 +30" "# which gives

# 3x = + 21" "# Finally divide both sides by 3

# (3x)/3 = 21/3# The answer is

#x = 7 #

To make sure the answer is correct, substitute the values for# x and y # into the other equation to check the answer:

#3x -5y =-29#

# 3 xx 7 - 5 xx 10 = - 29" " # this gives

# + 21 -50 = -29" "# adding the integers gives

# -29 = -29" "# The answer checks.