# a) If #x - 2y = -8#, and #3x - 6y = -12#, what are the values of #x# and #y#? b) How do you prove your answer from (a) graphically?

##### 1 Answer

a). The first step in solving by substitution is always solving for one of the variables. Since x in the second equation has coefficient

#x - 2y = -8 -> x = 2y - 8#

We now substitute this into the first equation.

#3(2y - 8) - 6y = -12#

#6y - 24 - 6y = -12#

#0y = 12#

This is true for no real value of

b). Let's do a little bit of work with the first equation.

#3x - 6y = -12#

We factor out a

#3(x - 2y) = -12#

Divide both sides by

#x - 2y = -4#

We get an equation that is identical to the second on the left-hand side, but different on the right-hand side. What does this mean?

Suppose we were to graph both lines. We would first convert to slope-intercept form.

#x - 2y = -4 -> -2y = -4 - x ->y = 1/2x + 2 #

For the second equation:

#x - 2y = -8 -> -2y = -8 - x -> y= 1/2x + 4#

These lines have equal slopes but different y-intercepts. This means that these are parallel lines, which is graphical proof that they will never intersect.

Hopefully this helps!