I know this is really easy but I have fogoton how to work with divisions in a simultanious equation. For example
(1) 10x - 8y = 7
(2) 3x -2y = 2
3x=2+2y
x=(2+2y)/3
what would you do next? How do you subsitute into 1?
2006-09-23 00:11:43 · 13 answers · asked by Siu02rk 3 in Science & Mathematics ➔ Mathematics
10x - 8y = 7
3x - 2y = 2
Multiply bottom by -4
10x - 8y = 7
-12x + 8y = -8
-2x = -1
x = (1/2)
10(1/2) - 8y = 7
5 - 8y = 7
-8y = 2
y = (-1/4)
x = (1/2)
y = (-1/4)
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the substitute method
10x - 8y = 7
3x - 2y = 2
3x - 2y = 2
3x = 2y + 2
x = (2y + 2)/3
x = (2/3)(y + 1)
10((2/3)(y + 1)) - 8y = 7
(20/3)(y + 1) - 8y = 7
Multiply everything by 3
20(y + 1) - 24y = 21
20y + 20 - 24y = 21
-4y + 20 = 21
-4y = 1
y = (-1/4)
3x - 2(-1/4) = 2
3x + (1/2) = 2
6x + 1 = 4
6x = 3
x = (1/2)
x = (1/2)
y = (-1/4)
2006-09-23 02:47:23 · answer #1 · answered by Sherman81 6 · 0⤊ 0⤋
The best way to solve this type of problem is to look at equations 1 and 2 and see what manipulation you can apply to one equation so that it contains equal numbers of the unknown x or y as in the other equation.
Therefore, we can see that if we simply multiply equation 2 by 4, we have:
12x - 8y = 8 lets call this equation 3.
If we now subtact equation 1 from equation 3, we will eliminate y. So:
2x = 1 ie x =1/2
Now use any of the 3 equations to substitute the now known x to find y. eg using equation 2:
3/2 - 2y = 2, therefore y = -1/4
2006-09-24 03:50:31 · answer #2 · answered by ? 7 · 0⤊ 0⤋
You are off to a good start but you need to understand the entire process. If you have only one equation containing x and y you can not find the value of x unless someone gives you the value of y. But if you are in possession of two equations (simultaneously!) that contain two variables (x and y) you can find the value of x in terms of y (as you did) from one equation and plug that (complex) value into the second equation wherever x appears leaving on y's. So you can then solve for y (which will be a numerical value ... half the problem solved!) and plug that number into the other equation wherever there is a y leaving only x's. You can now solve for the numerical value of x. You will then know what both x and y equal (problem solved). If there are three variables (x, y and z) you will need to have three equations (simultaneously!). Each equation must be unique (a different line on a graph) to work. Taking your equation (3x -2y = 2) and multiplying each term by say 2 (6x -4y = 4) would not be unique and would not help. Good luck.
2006-09-23 01:12:50 · answer #3 · answered by Kes 7 · 0⤊ 0⤋
p = a + 5 164 = 8a + 9p replace p = a + 5 into the backside equation - - - - - - - - - - - - - - - - - - - 164 = 8a + 9p 164 = 8a + 9(a + 5) 164 = 8a + 9a + 40 5 The distributive property on the final ingredient 164 = 17a + 40 5 gathering like words 164 - 40 5 = 17a + 40 5 - 40 5 Subtracting - 40 5 from the two aspects of the equation 119 = 17a 119/17 = 17a/17 Dividing the two aspects of the equation by using 17 7 = a Insert the a value into the equation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - fixing for p P = a + 5 p = 7 + 5 p = 12 Insert the p value into the equation 164 = 8a + 9p 164 = 8(7) + 9(12) 164 = fifty six +108 164 = 164 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - the respond is: a = 7 p = 12
2016-12-12 13:29:17 · answer #4 · answered by ? 3 · 0⤊ 0⤋
Therefore 10(2+2y)/3 - 8y = 7
So 20/3 + 20y/3 - 8y = 7
So (20/3 - 8)y = 7 - 20/3 = 1/3
So (-4/3)y = 1/3
So -4y = 1
So y = -1/4
So x = (2+2y)/3 = (2-2/4)/3 = 1/2
Checking result:
10(1/2) - 8(-1/4) = 5 + 2 = 7
3(1/2) - 2(-1/4) = 3/2 + 1/2 = 2
So x = 1/2, y = -1/4.
2006-09-23 00:31:31 · answer #5 · answered by David Y 5 · 1⤊ 0⤋
x = 1/2, y = -1/4
substitute as follows
10x - 8y = 7
=> 10 (2+2y)/3 - 8y = 7
=> 20 + 20y - 24y = 21 (x3 and expand out)
=> 20 - 4y = 21
=> 4y = -1
=> y= -1/4
put this value into (2) and you get x=0.5
2006-09-23 00:27:52 · answer #6 · answered by Freelancer 2 · 1⤊ 1⤋
sub value you obtained for x into (1)
10((2+2y))/3-8y=7
mult by 3
20+20y-24y=21>>>-4y=1>>>>>>>> y= -1/4
sub value for y into (2)
3x-(-1/2)=2>>>>>> 3x=3/2 >>>>>>> x=1/2
aliter
30x-24y=21 mult (1) by 3
30x-20y=20 mult (2) by 10 subtract -4y=1>>>> y= -1/4
sub in second equation
30x+5=20>>>>>>> x= 1/2
cheers,richard
2006-09-24 03:53:42 · answer #7 · answered by Anonymous · 0⤊ 0⤋
get the x of (1) and (2) so (1) x=(8y+7)/10 and (2) (2y+2)/3
and then put them into equation (8y+7)/10=(2y+2)/3 and then the cross of multiplication and then you can get now the value of y and also the value of x. thats it
2006-09-23 00:24:36 · answer #8 · answered by Anonymous · 0⤊ 1⤋
Cheat! I have an A at A Level in Maths but I ain't going to help u. x
2006-09-23 00:44:25 · answer #9 · answered by renaultfi69 2 · 0⤊ 0⤋
Check previous answers in this section on sim. equations
2006-09-23 00:14:17 · answer #10 · answered by ljcraigboy 2 · 0⤊ 2⤋