Solve algebraically the simultaneous equations: 6m + n = 16 and 5m - 2n = 19

The first step of solving simultaneous equations with two unknown variables (m & n in this case) is to rearrange one of the equations so that we get one variable in terms of the other. Lets take the first equation. We can rearrange this to n = 16 - 6m by subtracting 6m from both sides of the equal sign. Now we can substitute this value of n into the second equation, creating 5m - 2 * ( 16 - 6m ) = 19. We now have an equation which is entirely in terms of m, so we can simplify this down by multiplication and subtraction to 5m - 32 + 12m = 19 and then to 17m = 51. If we divide both sides by 17, we get m = 3. Substituting this value of m into the first equation gives 6 * 3 + n = 16, which simplifies to n = -2 by similar arithmetic.