How do you solve the simultaneous equations #2x + 3y = 9# and #3x + 2y = 1#?

1 Answer
Jul 30, 2015

Answer:

Multiply each equation by a (different) constant so the coefficients of #x# (or #y#) are identical then subtract one equation from the other to isolate a single variable.
#(x, y) = (-3, 5)#

Explanation:

[1]#color(white)("XXXX")##2x+3y = 9#
[2]#color(white)("XXXX")##3x+2y=1#

Multiply [1] by 2 and [2] by 3 to get
[3]#color(white)("XXXX")##4x+6y =18#
[4]#color(white)("XXXX")##9x+6y = 3#

Subtract [4] from [3]
[5]#color(white)("XXXX")##-5x = 15#

Solve for #x# by dividing [5] by #(-5)#
[6]#color(white)("XXXX")##x = -3#

Substitute #(-3)# for #x# in [1] to solve for #y#
[7]#color(white)("XXXX")##2(-3) + 3y = 9#

[8]#color(white)("XXXX")##3y = 15#

[9]#color(white)("XXXX")##y = 5#