How do you find the solution of the system of equations #5x - 2y = 4 # and #3x + y = 9 #?

1 Answer
May 5, 2018

Answer:

Find the value of one variable, and use that to solve for the other: See below.

Explanation:

A system of equations can technically be solve via one of 2 methods: elimination (I won't explain that here, since it is impractical, and I don't know that one too well; it makes your life necessarily difficult); substitution, where you isolate one of the variables in either equation (let's say you isolate #x#), and replace #x# in the other equation with the expression that you determined equals #x#. Graphing is good if you're in a pinch, but useless if you don't have a graphing calculator!

I'll demonstrate below:

Substitution (personal recommendation)

Step 1: Isolate one variable in one of the equations

#5x-4y=4#
#3x+y=9#

#5x cancel(-4y) color(blue)(+4y) = 9 color(blue)(+4y)#

#5x color(green)(-9) = cancel(9)+4y color(green)(-9)#

#5/4x-9/4=color(red)(cancel(4)/4)y#

#5/4x-9/4=y#

Now replace #y# in the other equation with #5/4x-9/4#, and solve for #x#

#3x+5/4x-9/4=9#

#12/4x+5/4x-9/4=9#

#17/4x=36/4+9/4#

#17/4x=45/4#

#x=45/4 div17/4#

#x=(45times4)/(4 times17)#
#x=(45timescancel4)/(cancel4 times17)#

#x=45/17#

And solve for #y#

#3(45/17)-9=y#

#x=45/17# and #y=-18/17#

Hope that helps!