Solve the following simultaneous equations: 4x+y=10 and 2x-3y=19

To begin to solve this question, we need to re-arrange the equations presented so they both appear in terms of 3y=. This will allow us to get a value for y and thus a value for x. First re-arrange the first equation into the form y=10-4x. From here, times both sides of the equation by 3 (not changing the fundamental relationship between any of the terms) to give us 3y=30-12x. We then rearrange the second equation into analogous terms, getting 3y=2x-19. By then replacing 3y in the first equation with its value in the second equation we get 2x-19=30-12x. We then add 12x and 19 to both sides, giving us 14x=49. From this we get x=3.5 and by plugging this into our equations, we get y= -4.