Give the solution:
2x-5y=5
10x-5y=20
I think there may be no solution but keep coming up with different alternatives. Please helllllllllllllp!!
2007-10-11 05:44:36 · 9 answers · asked by It's a girl due 5/11/09 4 in Science & Mathematics ➔ Mathematics
There is a solution... Here's some different ways to do it..
1. Graphically
2x-5y=5 manipulate to get... y=2/5x-1
10x-5y=20 manipulate to get y=2x-4
Graph the two lines. Where they intersect is the solution.
2. Substitution.
from 10x-5y=20 we can divide both sides by 5. Then solve for y by adding y to both sides and subtracting 4 from both sides.
Thus y=2x-4. Now substitute 2x-4 for y into the first equation to give... 2x-5(2x-4)=5 which is 2x-10x+20=5 which is -8x+20=5 which is -8x=-15 so x=15/8
Then put 15/8 into either equation for x to get y.
2(15/8)-5y=5 is 30/8-5y=5 is 6/8-y=1 is y=6/8-1 is y=6/8-8/8 is y=-2/8 is y=-1/4
3. Matricies
10 -5 20
2 -5 5
Subtract and get...
8 0 15
Divide by 8 and get
1 0 15/8 so x=15/8
for y
2 -5 5
10 -5 20
Multiply first line by 5
10 -25 25
10 - 5 20
Subtract
0 -20 5
divide by -20
0 1 -5/20 so y =-5/20=-1/4
done
2007-10-11 06:05:04 · answer #1 · answered by zenock 4 · 0⤊ 0⤋
Solve for 5y in the first one.
2x - 5y = 5
becomes
2x - 5 = 5y
Plug that into the second equation.
10x-5y=20
becomes
10x - (2x - 5) = 20
Distribute the negative sign.
10x - 2x + 5 = 20
8x + 5 = 20
8x = 15
Solve for x. Plug x back into the first equation.
2007-10-11 06:00:15 · answer #2 · answered by Brian L 7 · 0⤊ 0⤋
The only problem is that you get values which are fractions or decimals. Subtracting
8x = 15. x = 1 7/8 or 1.875, Substituting for x
15/4 - 5y = 5 or 5y = - 5/4 or y = -1/4 or( - 0.25).
2007-10-11 05:54:48 · answer #3 · answered by Pandian p.c. 3 · 0⤊ 0⤋
Subtract the bottom eq from the top and get
-8x = -15
x = 15/8
Mult the top eq. by 5 and get
10x-25y=25
10x-5y =20
Now subt the bottom one from the top
-20y=5
y=-5/20
y=-1/4
Check by subst. back the values into the eq.
2(15/8)- 5(-1/4) = 5
30/8+5/4 =5
15/4 +5/4 =5
20/4 = 5
5=5 Check
Subst. into the other eq.
10(15/8) - 5(-1/4) =20
20=20 check
2007-10-11 05:50:23 · answer #4 · answered by Anonymous · 2⤊ 0⤋
1st equation says -5y = 5-2x
2nd equation says -5y = 20 -10x
Therefore 5-2x = 20 -10x since they both = -5y
So 8x = 15 and x = 15/8
y = (2x-5)/5 = -1/4
2007-10-11 05:57:15 · answer #5 · answered by ironduke8159 7 · 0⤊ 0⤋
Well, you have two equations and two unknowns, so you can solve it
Using Gaussian elimination
[2 -5 5]
[10 -5 20]
-R2+R1
[-8 0 -15]
[10 -5 20]
-1/8R1, -10R1+R2, -1/5R2
[1 0 15/8]
[0 1 -1/4]
So x=15/8 and y=-1/4
2007-10-11 05:58:23 · answer #6 · answered by Anonymous · 0⤊ 0⤋
x = 15/8
y = - 1/4
2007-10-11 05:50:47 · answer #7 · answered by ollie_ho 3 · 0⤊ 0⤋
subtract 1st equation from 2nd gives
8x=15, thus x = 15/8
show me how you got different alternatives, i want to laugh ;)
'
2007-10-11 05:48:15 · answer #8 · answered by gjmb1960 7 · 0⤊ 1⤋
subtract these 2
8x=15
x=15/8
2007-10-11 05:47:54 · answer #9 · answered by Anonymous · 0⤊ 0⤋