How do you solve #2x + 6y = 2# and #x + 5y = 3# using matrices?

1 Answer
Oct 23, 2016

Answer:

#(x,y)=(-2,1)#
(see below for solution using matrices).

Explanation:

Write the given equations
#color(white)("XXX")2x+6y=2#
#color(white)("XXX")x+5y=3#
in augmented matrix form
#color(white)("XXX")( (2,6,2),(1,5,3))#

Divide the first row by #2#
#color(white)("XXX")((1,3,1),(1,5,3))#

Subtract the (new) first row from the second row
#color(white)("XXX")((1,3,1),(0,2,2))#

Divide the (new) second row by #2#
#color(white)("XXX")((1,3,1),(0,1,1))#

Subtract #3# times this second row from this first row
#color(white)("XXX")((1,0,-2),(0,1,1))#

Note that this is equivalent to the expressions
#color(white)("XXX"){: {:(1x,+0y,=-2),(0x,+1y,=1):}} rArr {:(x=-2),(y=1):}#