2007-09-09 07:58:49 · 8 answers · asked by manhattanbrat 1 in Science & Mathematics ➔ Mathematics
5y-6=3(y-x)-2
5y - 6 = 3y - 3x - 2
5y - 3y = -3x + 6 -2
2y = -3x + 4
y = -3x/2 + 2
2007-09-09 08:06:00 · answer #1 · answered by Runa 7 · 0⤊ 0⤋
multiply this out
5y - 6 = 3*(y-x) - 2
5y - 6 = 3y - 3x - 2
now we want to get the variable y all on one side. you can add/subtract/multiply/divide an equation, so long as you do the same thing to both sides, and maintain the equality. We want to get the multiplier for y equal to 1.
5y - 6 = 3y - 3x -2
5y - 6 + 6 = 3y - 3x - 2 + 6
5y = 3y - 3x + 4
5y - 3y = 3y - 3x + 4 - 3y
2y = -3x + 4
2y/2 = (1/2)*(-3x + 4)
y = (-3/2)*x + 2
y = 2 - (3/2)*x
Now lets find a value for x by subsituting our answer above for y into the original equation:
5y - 6 = 3*(y-x) - 2
5y - 6 = 3y - 3x - 2
5*(2 - (3/2)*x) - 6 = 3*(2 - (3/2)*x) -3x - 2
10 - (15/2)*x - 6 = 6 - (9/2)*x - 3x - 2
4 - (15/2)*x = 4 - (9/2)*x - (6/2)*x
4 - (15/2)*x = 4 - (3/2)*x
4 - (15/2)*x - 4 = 4 - (3/2)*x - 4
(-15/2)*x = (-3/2)*x
which only works if x=0
now plug x into our solution for y previously, to get y:
y = 2 - (3/2)*x
y = 2 - (3/2)*0
y = 2
now lets check that y = 2 and x = 0 works in the original equation:
5y - 6 = 3*(y-x) - 2
5*2 - 6 ?= 3*(2-0) -2
10 - 6 ?= 3*2 - 2
4 ?= 6 -2
4 = 4 yea! it works.
2007-09-09 08:32:23 · answer #2 · answered by mrvadeboncoeur 7 · 0⤊ 0⤋
since you have 2 unknowns x,y and only 1 equation you can only solve for y in terms of x. if you were given a second equation then we could find a numerical value for x & y.
5y-6=3(y-x)-2
5y -6 = 3y -3x -2
5y - 3y = 4 - 3x
2y = 4 -3x
y = 2 - 3x/2
2007-09-09 08:11:24 · answer #3 · answered by 037 G 6 · 1⤊ 0⤋
5y-6=3(y-x)-2 Isolate variables of either side of equation.
5y-6=3(y-x)-2
5y-6+2=3(y-x)-2+2
5y-4=3(y-x)
(5y-4)/3=3(y-x)/3
(5y-4)/3=y-x because we are dividing, give each part on top its own denominator (the value under the / sign) and give identies for the opposite side.
(5y/3)-(4/3)=(3y/3)-(3x/3)
(5y/3)-(4/3) -(3y/3)=(3y/3)-(3x/3) -(3y/3)
(2y/3)-(4/3)=-x
ok we solved it for -x but we want y alone. now get y alone.
(2y/3)-(4/3)=-x
(2y/3)-(4/3) +(4/3)=-x+(4/3)
(2y/3)=-x+(4/3)
(2y/3)*(3/2)=[-x+(4/3)]*(3/2)
y=(3/2)*-x+(4/3)*(3/2)
simplify equation
y=(-3x/2)+(4*3/3*2)
y=(-3x/2)+(12/6)
y=(-3x/2)+2
so your solution to this problem is y=(-3x/2)+2
EDIT: lost a negative sign, sorry
2007-09-09 08:11:09 · answer #4 · answered by bozman19161 2 · 1⤊ 0⤋
5y - 6 = 3(y - x) -2
5y - 6 = 3y - 3x -2
2y = -3x + 4
y = -3/2(x) + 2
(0, 2)
(2, -1)
2007-09-09 08:07:45 · answer #5 · answered by Anonymous · 1⤊ 0⤋
5y-6=3(y-x)-2
5y-4= 3(y-x)
y= 5
x= -2
2007-09-09 08:12:40 · answer #6 · answered by rach 2 · 1⤊ 0⤋
y = (-3x+4)/2
2007-09-09 08:07:23 · answer #7 · answered by Anonymous · 1⤊ 0⤋
5y-6=3(y-x)-2
5y-6=3y-3x-2
5y=3y-3x-2+6
5y-3y=-3x-2+6
2y=4-3x
y=(4-3x)/2
2007-09-09 08:09:28 · answer #8 · answered by samuraidragon101 2 · 1⤊ 0⤋