How do you solve the system using the elimination method for 3a + 4b = 2 and 4a - 3b = -14?

1 Answer
Jul 8, 2015

Answer:

#(a,b) = (-2,2)#

Explanation:

Given
[1]#color(white)("XXXX")##3a+4b=2#
[2]#color(white)("XXXX")##4a-3b = -14#

Multiply [1] by 4 and [2] by 3 to obtain two equations with the same #a# coefficient
[3]#color(white)("XXXX")##12a+16b = 8#
[4]#color(white)("XXXX")##12a-9b=-42#

Subtract [4] from [3] to clear the #a# term
[5]#color(white)("XXXX")#25b= 50#

Divide both sides by #25#
[6]#color(white)("XXXX")##b =2#

Substitute #b=2# into equation [1]
[7]#color(white)("XXXX")##3a+4(2) = 2#

[8]#color(white)("XXXX")##3a = -6#

[9]#color(white)("XXXX")##a = -2#