Putting Equations in standard form (Ax+By=C form)?

These two:





1. y - 1 = 1.5(x + 3)





2. y + 6 = -3.8(x - 2)





Please show work.





My daughter is doing it the x10 to get rid of decimal then divide by 10 at the end, but she's not sure what to do with the y when she does that???

Putting Equations in standard form (Ax+By=C form)?
y - 1 = 1.5(x + 3)





y - 1 = 1.5x + 4.5





-1.5x + y - 1 = 4.5





-1.5x + y = 5.5





------





y + 6 = -3.8(x - 2)





y + 6 = -3.8x + 7.6





3.8x + y + 6 = 7.6





3.8x + y = 1.6
Reply:to answer your question, i'd like to solve the first one





1. y - 1 = 1.5 (x+3)





now you're stating that she multiplies each side by 10 so...





10 * (y-1) = 10 * 1.5 * (x+3)





10 (y-1) = 15 * (x+3)





from here, she must distribute the 10 and the 15 on the left and right sides respectively





10 (y-1) = 15 * (x+3)





10*y- 10 * 1 = 15*x + 15 * 3





10y - 10 = 15x + 45





from what you've said, I think she's got it up to here


now she would need to get the variables, x and y, on one side of the equation, and the constants on the other





first, lets get the constants on one side of the equation


two ways to do it, both work:





a. add ten to both sides to cancel out the -10 on the left side of the equation





10y - 10 = 15x + 45


10y - 10 + 10 = 15x + 45 + 10


10y = 15x + 55





or





b. subtract 45 from each side to cancel out the 45 on the right hand side of the equation





10y - 10 = 15x + 45


10y - 10 - 45 = 15x + 45 - 45


10y - 55 = 15x





since all the constants are on one side in either case, now one must get all the variables to one side


**a. and b. are the last steps from previous a. and b.**





a. in this case, the constant, 55 is on the right. thus, the variables must be put on the left side of the equation. if you look on the right hand side, there is a 15x. to cancel this out, subtract 15x from both sides





10y = 15x + 55


10y - 15x = 15x - 15x + 55


10y - 15x = 55





***note: if i recall correctly, in standard form, there must be a positive constant before x. currently, it is -15. to make this positive, multiply both sides of the equation by -1





10y - 15x = 55


-1 * (10y - 15x) = -1 * 55


-10y + 15x = -55


15x -10y = -55





or





b. here, we have the opposite case of what was above. here the constant is on the left, so the variables must brought to the right hand side of the equation. to do this, subtract 10y from each side





10y - 55 = 15x


10y - 10y - 55 = 15x - 10y


-55 = 15x - 10y





***notice that both method a. and b. both are the same at this point. also notice that the constant before x, 15, is positive, and thus one does not need to multiply by the -1





from here the next step is to simplify as much as one can. some teachers may accept above equation as is for a time, but most want it simplified as much as possible





remember how in fractions, one looks for the greatest common factor and simplifies by it (ex. 12/3, the greatest common factor is 3, 12/3 = 4, 3/3 = 1, thus the fraction reduces to 4/1 or 4) the same principle is applied when solving equations





one must look at the equation and determine what the greatest common factor is to both sides of the equation





15x -10y = -55





looking at it, one might immediately tell that it is 5, if not, factor each constant, 15, 10, and -55


they factor into:


15: 3, 5


10: 2, 5


-55: -1, 5, 11





only one common to each is 5, thus 5 is the number you're looking for





divide each side by the greatest common factor, 5, to finally simplify the equation as much as is possible





15x - 10y = -55


(15x - 10y)/5 = -55/5


15x/5 - 10y/5 = -55/5


3x - 2y = -11





hope are able to tell what to do from that explanation, if not, feel free to message. I will help as much as I can.