algebra help?

Question

i am having trouble with this question. i have to solve each equation with the subsitution method.

3(y-1)=2(x-3)
3y-2x=-3

i get as far as y=2x and x= -3/4 am i on the right track? please show how you get to the answer

Answer 1

3(y-1)=2(x-3)
3y-3=2x-6
3y-3+6=3y+3=2x
1.5y+1.5=x On to the next equation
3y-2(1.5y+1.5)=-3
3y-3y-3=-3
-3=-3
In actuality both equations are for the same line. Start with the first equation 3(y-1)=2(x-3).
Then 3y-3=2x-6 after removing ()
So 3y=2x-3 after adding 3 to both sides
Then after subtracting 2x from both sides you get 3y-2x=-3 which is the second equation.
So the two equations are the same line. All points are common.
3y=2x-3 yields
y=2/3*x-1
So you have (with either of your two original equations) a single line with a slope of 2/3, an x intercept of -1 and a y intercept of 1.5.

Answer 2

3(y - 1) = 2(x-3), 3y - 2x = -3
simplfy and put both equations in y = mx + b
first equation
3y - 3 = 2x - 6 ~> 3y = 2x - 3 ~> y = 2/3x - 1
second equation
3y - 2x = -3 ~> 3y = 2x - 3 ~> y = 2/3x - 1
(note: the equations end up being the same, so the solution is going to be all real numbers (AR#))

both equations have y by itself with a coefficient of 1, so you can set them equal to each other and solve for x, then plug the x value back into the original equations to find y
2/3x - 1 = 2/3x - 1
add 1 to both sides
2/3x = 2/3x
subtract 2/3x from bith sides
0 = 0
that is a true statement which means that all real values satisfy the system

Answer 3

Solve equation 2 for x:

2x = 3y + 3
x = 1.5y + 1.5

Plug in:

3(y - 1) = 2(1.5y + 1.5 - 3)
3y - 3 = 3y + 3 - 6
3y - 3 = 3y - 3

These two equations are the same equation, stated differently. There is no way to solve for x or y.

Answer 4

simplify each first

3(y-1) = 2(x-3) ...so..... 3y -3 = 2x - 6 and 3y = 2x -3

Then 3y - 2x = -3

notice the first equation looks exactly like the second so this represents the same function with an infinite number of solutions.

Answer 5

Using the original equation, factor out (multiply the coefficient throughout the parentheses). Then solve for one of the variables in terms of the other. Your answer should have a variable without a coefficient on one side, (x=?). When you get that, just substitute the other side of the resulting equation (the ? part) into the original equation. That way, you should only have one variable throughout the equation. Then solve the variable until you get a number as the result. Finally, substitute that number into the original equation to get the other variable. Finally, plug in your two numeral answers to check out if they're right.

Hope this walkthrough helps =). Didn't want to solve the thing for you =P

Answer 6

3(y-1)=2(x-3) - Eq. No. 1

3y - 3 = 2x - 6

3y - 2x = -6 + 3 = -3

So, your equation is correct upto that point.

If 3y - 2x = -3

y = 2x/3 - 1 and not what you got.