How do you solve 9x -2y = 28 and y= -3x + 1?

1 Answer
Oct 13, 2015

Answer:

#{(x=2), (y = -5) :}#

Explanation:

Your starting system of equations looks like this

#{(9x - 2y = 28), (y = -3x + 1) :}#

Notice that you can rearrange the second equation to get the #x# and #y# terms on the left-hand side of the equation

#{(9x - 2y = 28), (3x + y = 1) :}#

Another thing to notice here is that if you multiply the second equation by #2#, and add the left-hand sides and right-hand sides of the two equations separately, you can cancel out the #y# term.

This will allow you to find the value of #x#.

#{(9x - 2y = 28), (3x + color(white)(x)y = color(white)(x)1 | xx 2) :}#

#{ (9x - 2y = 28), (6x + 2y = color(white)(x)2) :}#

Now add the two equations as described above

#{ (9x - 2y = 28), (6x + 2y = color(white)(x)2) :}#
#color(white)(x)stackrel("-------------------------------")#

#9x - color(red)(cancel(color(black)(2y))) + 6x + color(red)(cancel(color(black)(2y))) = 28 + 2#

#15x = 30 implies x = 30/15 = color(green)(2)#

Now use this value of #x# into one of the two equations to get the value of #y#

#3 * (color(green)(2)) + y = 1#

#y = 1 - 6 = color(green)(-5)#

The solution set for this system of equations will be

#{(x=2), (y = -5) :}#