Caprice adds equations A and B to solve this system of equations. What makes this approach a valid method in general for solving a system of equations?
Equation A:
Equation B:
8x + 3y = 27
4x - 3y = 9
12x = 36
CLEAR
CHECK
The method will give the correct solution, x = 3 and y = 1
8(3) + 3(1) - 27
4(3)-3(1) = 9
As long as addition used on both sides or subtraction is
used on both sides, a true equation will remain true.
Because the y-terms cancel:
(8x + 3y) + (4x - 3y) - 8x + 4x + 3y - 3y = 12x
Adding a quantity like 8x + 3y to one side of an equation
and another quantity like 27 to the other side maintains
the equality if the two quantities are equal.