How do you solve the system of equations: 5m + 2n = -8 ; 4m + 3n = 2?

1 Answer
Aug 21, 2015

Answer:

#(m,n) = (-4,6)#

Explanation:

[1]#color(white)("XXXX")5m+2n=-8#
[2]#color(white)("XXXX")4m+3n = 2#

Multiply [1] by 3, then [2] by 2, generating two equations with the same coefficient for #n#
[3}#color(white)("XXXX")15m+6n= -24#
[4]#color(white)("XXXX")8m+6n=4#

Subtract [4] from [3]
[5]#color(white)("XXXX")7m = -28#

Divide both sides by 7
[6]#color(white)("XXXX")m = -4#

Substitute #(-4)# for #m# in [1]
[7]#color(white)("XXXX")5(-4)+2n = -8#

Simplify
[8]#color(white)("XXXX")2n = 12#

Divide by 2
[9]#color(white)("XXXX")n = 6#