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

1 Answer
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.