How do you determine the solution in terms of a system of linear equations for #5x + 2y = 5#, #3x + y = 2#?

1 Answer
Sep 23, 2015

Answer:

#x=-1#
#y=5#

Explanation:

You can solve for the solution using elimination or substitution. Personally, I think it will be easier to use substitution for this problem, so that's what I will use.

First, let's look at the second equation. You will notice that it is easy to isolate #y# here.
#3x+y=2#
#3x+y-3x=2-3x#
#color(red)(y=2-3x)#

Now that we've isolated #y# in the second equation, we will now substitute this into #y# in the first equation.
#5x+2color(red)y=5#
#5x+2color(red)((2-3x))=5#
#5x+4-6x=5#
#4-x+x=5+x#
#4=5+x#
#4-5=5+x-5#
#-1=x#
#color(blue)(x=-1)#

Now that we have solved for the value of #x#, let's go back to the equation earlier where we isolated #y#.
#color(red)(y=2-3)color(blue)x#
#y=2-3color(blue)((-1))#
#y=2+3#
#color(red)(y=5)#

So the solutions are: #color(blue)(x=-1)# and #color(red)(y=5)#.

Checking
In case you are unsure of your answer, you can check this by substituting the solutions in both of the equations.
#5color(blue)x+2color(red)y=5#
#5color(blue)((-1))+2color(red)((5))=5#
#-5+10=5#
#color(magenta)(5=5)#

#3color(blue)x+color(red)y=2#
#3color(blue)((-1))+color(red)((5))=2#
#-3+5=2#
#color(magenta)(2=2)#