Question
Trying to solve paired linear equations, like the following,by solving for Y and then substituting back in for X. Troubleis, when I pull out the X's to solve for Y, the Y's are going awayalso: -2X + Y = 6 4X - 2Y = 12 I have multiplied the top equation by 2, then added bothequations--but the X's AND the Y's drop out: everything goesto zero. What should I do? Trying to solve paired linear equations, like the following,by solving for Y and then substituting back in for X. Troubleis, when I pull out the X's to solve for Y, the Y's are going awayalso: -2X + Y = 6 4X - 2Y = 12 I have multiplied the top equation by 2, then added bothequations--but the X's AND the Y's drop out: everything goesto zero. What should I do?
Explanation / Answer
After multiplying the top equation by 2 which makes it -4x+2y= 12 and adding that to 4x-2y=12 you would get 0=24 (don't forget12+12 as it seems you did) and since that is a false statement,there is no solution for this system. Also, even without solving the system you can tell there areno solutions because the two lines are parallel and therefornever intersect. They're parallel the have the same slopebut different y-intercepts. You know this because in standard formof an equation: ax+by=c the slope is -a/b and the y-intercept isc/b. So the slope of -2x + y =6 is 2/1 or just 2 and the slope of4x-2y=12 is -4/-2 which reduces to 2 as well. The y-intercept ofthe first equation is 6/1 or just 6 and the y-intercept of theother equation is 12/-2 which is -6. Different y-intercept, sameslope.