How do you solve for linear system equations?

Answer 1

Simple systems of linear equations involve two equations and two variables. Graphically this may be represented by the intersection of lines in a plane. If the two equations describe the same line or parallel lines, there is no solution.

Example:

x + y = 7

2x - y = 8

We might rewrite the first equation as x = 7 - y (subtracting y from each side).

Then we can substitute 7-y for x in the second equation:

2(7-y) - y = 8

By the distributive property of multiplication over addition this yields:

14 - 2y - y = 8

14 - 3y = 8 (combining -2y and -y)

14 = 8 + 3y (add 3y to each side)

6 = 3y (subtract 8 from each side)

2 = y (divide each side by 2).

If y = 2, we can substitute this back into either equation. The first looks like it would be the easiest: x + 2 = 7.

x is therefore 5.