SOLUTION: Solve the equation.
4x-1 / x^2+5x-14 = 1/x-2 - 2/x+7
Solve the system of equations.
1.) y= -5x-2
y= -3x
2.) 3x - y = 5
-4x + y = -5
3.) 2x - y =
Algebra.Com
Question 32929: Solve the equation.
4x-1 / x^2+5x-14 = 1/x-2 - 2/x+7
Solve the system of equations.
1.) y= -5x-2
y= -3x
2.) 3x - y = 5
-4x + y = -5
3.) 2x - y = -1
2x + z = -6
3y - z = 7
I really need help on these problems I have done these problems over and over again until I am getting frustrated with myself. I need help. I am not sure if you are supposed to plug in the -3x into the other problem in question one. I am not sure if you are supposed to just add the x and y values and then solve for y in problem 2. Are you supposed to use cramers rule for problme three. Please help me I am struggling with these problems. I need somebody to help understand the process of each problem so I will understand the problems come test time on Monday. Thanks for your time and help it is greatly appreciated.
Hilary
Found 2 solutions by checkley71, stanbon:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
(4x-1)/(x~2+5x-7)=1/(x-2)-2/(x+7) or (4x-1)/(x+7)(x-2)=1/(X-2)-2/(X+7) OR
(4X-1)/(X+7)(X-2)=((X+7)-(2X+4))/(X+7)(X-2) or 4x-1=x+7-2x+4 or 5x=12 or x=12/5
proof (4(12/5)-1)/(12/5)~2+5(12/5)-7=1/((12/5)-2)-2/((12/5+7) or
(48/5-1)/((12/5)~2+(12/5)+7)=1/((12/5)-2)-2/((12/5)+7) or 43/5=12/5+7-2(12/5)+4
or 43/5=12/5+7-24/5+4 or 43/5=12/5+11-24/5 or 43/5=-12/5+11 or 55/5=11 or 11=11
y=-5x-2
y=-3x substituting y=-3x in equation #1 we get
-3x=-5x-2 or 2x=-2 or x=-1 then y=-5(-1)-2 or y=+5-2 or y=3
proof 3=-3(-1) or 3=3 and 3=-5(-1)-2 or 3=5-2 or 3=3
3x-y=5
-4x+y=-5 adding these two equztions we get
--------
-x=0 substituting 0 for y in equation #1 we get
3*0-y=5 or y=-5
proof -4*0-5=-5 or -5=-5 and 3*0-(-5)=5 or 5=5
2x-y=-1
2x+z=-6
3y-z=7 adding equation #2 & #3 we get
-------
2x+3y=1 subtracting this equation from equztion #1 we get
2x-y=-1
-2x-3y=-1
--------
-4y=-2 or y=1/2 then 2x-(1/2)=-1 or 2x=-1/2 or x=-1/4 therefore 3(1/2)-z=7 or
3/2-z=7 or -z=7-3/2 or z=-11/2
x=-1/4, y=1/2 & z=-11/2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
[(4x-1)/(x^2+5x-14)]=[1/(x-2)]-[2/(x+7)]
Factor where you can and get a common denominator on the right side as follows:
[(4x-1)/(x+7)(x-2)]= [(x+5)/(x-2)(x+7)]
Both denominators are the same so equate the numerators to get:
4x-1=x+5
3x=6
x=2
1)y=-5x-2
y=-3x
Substitute to get:
-3x=-5x-2
2x=-2
x=-1
Substitute again to get:
y=(-3)(1)
y=3
Solution: (-1,3)
2)
a)3x-y=5
b)-4x+y=-5
Rewrite as:
a)y=3x-5
b)y=4x-5
This is a contradiction. There is no solution
for this system of equations. The lines are
parallel and do not intersect.
3)Rewrite as follows:
2x-y+0z=-1
2x+0y+z=-6
0x+3y-z=7
And use Cramer.
I get x=-1/4; y=1/2; z=-11/2
Cheers,
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