How do you solve for linear system equations? - Answers

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.