How do i solve the following simultaneous equations: 4x - 2y = 2, 3x - y = 4?
Question:
Answers:
4x - 2y = 2
3x - y = 4
=>
4x - 2y = 2
6x - 2y = 8 ... -
-----------------
-2x = -6
x = 3
=>
3(3) - y = 4
-y = 4 - 9
y = 5
Answer: S = {(3, 5)}
Thats wrong, the answer is 6.
First, try to leave y alone within one side in both equations.
2y = 4x - 2
y = 3x - 4
Then, divide the first equation by two to hold y instead of 2y.
y = 2x - 1
See, in both equations "y" is equal to a funciton of x. So, we can assume them equal.
2x - 1 = 3x - 4
and solve this equation.
x = 3.
If you put this x effectiveness into either of the equations you have at the beginning, you will find the y expediency of your answer. Take the first one.
4 ( 3) - 2y = 2
y= 5
The answer is: (3,5)
First of all sign them 1 and 2
So equation 1: 4x - 2y = 2
and equation 2: 3x - y = 4
By rearranging 2, you capture y = 4 + 3x
Substitute this y-value into 1, and get 4x - 2(4 + 3x) = 2
multiply out the brackets: 4x - 8 + 6x = 2
so: 10x = 10
so: x = 1
Now substitute this into equation 2, so (3 x1) - y = 4
so 6 - y = 4
so y = 10
Therefore, x=1 and y= 10
4x-2y=2 so 4x = 2y +2 which finances x = 1/2 y + 1/2
the oher is 3x-y= 4, which means y= 3x-4 and after we sub them into the other equation
x = 1/2 y + 1/2 = x = 1/2 (3x-4) + 1/2 = 1.5x - 2 +.5 =x , so 1/2x = 1.5, so x = 3
y we put to get 3(3) -y =4 to go and get y = 5
4x-2y=2
-6x+2y=-8
adding
-2x=-6
x=3
sub
12-2y=2
-2y=-10
y=5
solution set {3,5}
x=3, y=5
4x - 2y = 2 ---(1)
3x - y = 4 ----(2)
(2)x2, 6x - 2y = 8 ---(3)
(3)-(1), 2x = 6 => x = 3
Substitute x=3 into (2),
3(3) - y = 4
9 - 4 = y
y = 5
4x -2y = 2
x = (2 + 2y) / 4
x = (1 + 1y) / 2
3x - y = 4
[ 3(1 + 1y) / 2 ] - y = 4
(3/2) + (3/2)y - y = 4
(1/2)y = 4-(3/2)
(1/2)y = (5/2)
y = 5
x = (1 + 1y) / 2
x = (1 + 1*5) / 2
x = 6 / 2
x = 3
With x & y solved, it will be:12-10=2, 9-5=4
x=3, y=5
This is correct.
oww!!
More Questions and Answers...