How do you solve #6x+9y=3# and #x+4y=-2#?

1 Answer
May 23, 2018

Answer:

See a solution process below:

Explanation:

Step 1) Solve the second equation for #x#:

#x + 4y = -2#

#x + 4y - color(red)(4y) = -2 - color(red)(4y)#

#x + 0 = -2 - 4y#

#x = -2 - 4y#

Step 2) Substitute #(-2 - 4y)# for #x# in the first equation and solve for #y#:

#6x + 9y = 3# becomes:

#6(-2 - 4y) + 9y = 3#

#(6 xx -2) - (6 xx 4y) + 9y = 3#

#-12 - 24y + 9y = 3#

#-12 + (-24 + 9)y = 3#

#-12 + (-15)y = 3#

#-12 - 15y = 3#

#-12 + color(red)(12) - 15y = 3 + color(red)(12)#

#0 - 15y = 15#

#-15y = 15#

#(-15y)/color(red)(-15) = 15/color(red)(-15)#

#y = -1#

Step 3) Substitute #-1# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:

#x = -2 - 4y# becomes:

#x = -2 - (4 xx -1)#

#x = -2 - (-4)#

#x = -2 + 4#

#x = 2#

The Solution Is:

#x = 2# and #y = -1#

Or

#(2, -1)#