How do you solve the following linear system: #-9x - 5y = -1, 3x + y = 1 #?

1 Answer

Answer:

There are two methods: Substitution and addition, subtraction.
For this problem addition or subtraction would be the preferred method.
#x = 2/3 and y = -1#

Explanation:

Multiplying the second equation by 3 makes adding the two equations easy

# 3 xx ( 3x + y = +1)# gives

#9x + 3y = +3 #

Now add the two equations

#-9x - 5y = - 1#
#ul(+9x +3y = +3)#
#" "0x - 2y = +2# This is what it gives

Now solve for y by dividing both sides by #-2 #

#( -2 y)/( -2) = (+2)/(-2)#

This gives #y = -1#

Put #- 1# into either equation for #y# and solve for #x#

#3x -1 = + 1 " "# Add + 1 to both sides of the equation

#3x - 1 +1 = +1 + 1 #

This gives

#3x = 2" "# Divide both sides by 3

# (3x)/ 3 = (+2)/3" "# This gives

#x = 2/3#

The point of intersection is #(2/3, -1 ) #

The substitution method would also work but in this case would be more difficult. An alternative would be to graph both equations and then find the point of intersection.