How do solve the following linear system?: #-7x + y = -19 , -2x + 3y = -19 #?

1 Answer
Jan 9, 2016

Answer:

#x=2# and #y=-5#

Explanation:

For a linear system with 2 different unknowns, we use
Substitution Equation to find the actual value of the unknown.

There are two unknowns, #x# and #y#.

Firstly, let #-7x+y=-19# as Equation 1
and #-2x+3y=-19# as Equation 2.

From one of the equation, for example Equation 1 we can rearrange a new equation and substitute it into the other equation.

Let say, from Equation 1,
#-7x+y=-19#
Rearrange the equation in terms of only one unknown.
#y=-19+7x# as Equation 3

Substitute Equation 3 into Equation 2 and we will get;
#-2x+3y=-19# given #y=-19+7x#,

#-2x+3(-19+7x)=-19#

#-2x-57+21x=-19#

#-2x+21x=-19+57#

#19x=38#

#x=2#

Substitute #x=2# into Equation 3 and we will get;
#y=-19+7x# given #x=2#

#y=-19+7(2)#

#y=-5#