How do you solve the following linear system: #-7x - 5y =4, -x + y = 21 #?

1 Answer
Hugo C.
Nov 14, 2015

#x = 101/12#,

#y = 353/12#.

Explanation:

We start with:
#- 7x - 5y = 4#,
#- x + y = 21#.

There are three ways of solving these problems. I'll choose substitution, as I find it easier. Let's start. First of all, we leave #x# or #y# alone in any of the #2# equations. So,
#-x + y = 21#,
#y = x + 21#.

We now substitute this into the other equation:
#- 7x - 5(x + 21) = 4#,
#- 7x -5x + 105 = 4#,
#- 12x = -101#, Which we can write as:
#12x = 101#
#x = 101/12#.

We now substitute this into any of the equation. I'll choose the second one:

#- 101/12 + y = 21#,
#y = 21 + 101/12#
#y = 353/12#.

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