How do you solve the system of equations #7x + 3y = - 9# and #3y = x + 15#?

1 Answer
Jan 25, 2018

See a solution process below:

Explanation:

Step 1) Solve each equation for #3y#:

  • Equation 1:

#7x + 3y = -9#

#7x - color(red)(7x) + 3y = -9 - color(red)(7x)#

#0 + 3y = -9 - 7x#

#3y = -9 - 7x#

  • Equation 2: is already solved for #3y#

#3y = x + 15#

Step 2) Because the left side of both equations are equal we can equate the right sides of the equations and solve for #x#:

#-9 - 7x = x + 15#

#-9 - color(blue)(15) - 7x + color(red)(7x) = x + color(red)(7x) + 15 - color(blue)(15)#

#-24 - 0 = 1x + color(red)(7x) + 0#

#-24 = (1 + color(red)(7))x#

#-24 = 8x#

#(-24)/color(red)(8) = (8x)/color(red)(8)#

#-3 = (color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8))#

#-3 = x#

#x = -3#

Step 3) Substitute #-3# for #x# in either of the equations from Step 1 and solve for #y#:

#3y = x + 15# becomes:

#3y = -3 + 15#

#3y = 12#

#(3y)/color(red)(3) = 12/color(red)(3)#

#(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = 4#

#y = 4#

The Solution Is:

#x = -3# and #y = 4#

Or

#(-3, 4)#