4x+6y=1/8+3x+7y=1/10
Poorly written.
I bet you mean:
4x+6y=1/8
3x+7y=1/10
multiply the first by 3 ----> 12x + 18y = 3/8
multiply the 2nd by 4 ----> 12x + 28y = 2/5
subtract the new first from the new 2nd
10 y = 2/5 - 3/8 = 1/40
y = 1/400
sub into original first equation:
4x+6(1/400)=1/8 <---- multiply everybody by 400
1600x + 6 = 50
x = 44/1600 = 11/400
4 x + 6 y = 1 / 8 + 3 x + 7 y = 1 / 10
mean:
4 x + 6 y = 1 / 10
1 / 8 + 3 x + 7 y = 1 / 10
Rewrite second equation:
1 / 8 + 3 x + 7 y = 1 / 10
Subtract 1 / 8 to both sides
1 / 8 + 3 x + 7 y - 1 / 8 = 1 / 10 - 1 / 8
3 x + 7 y = 1 / 10 - 1 / 8
3 x + 7 y = 4 ∙ 1 / 4 ∙ 10 - 5 ∙ 1 / 5 ∙ 8
3 x + 7 y = 4 / 40 - 5 / 40
3 x + 7 y = - 1 / 40
Now you must solve system of two equations:
4 x + 6 y = 1 / 10
3 x + 7 y = - 1 / 40
Try that.
The solutions are:
x = 17 / 200 , y = - 1 / 25
Reiny may be right.
Really what does 4 x + 6 y = 1 / 8 + 3 x + 7 y = 1 / 10 mean?
To solve the system of equations:
4x + 6y = 1/8 (Equation 1)
3x + 7y = 1/10 (Equation 2)
There are several methods to solve this system of equations, such as substitution, elimination, or using matrices. Let's use the substitution method to find the solution.
First, we solve Equation 1 for x:
4x = 1/8 - 6y
x = (1/8 - 6y) / 4
Now substitute x in Equation 2 with (1/8 - 6y) / 4:
3 * ((1/8 - 6y) / 4) + 7y = 1/10
To simplify further, let's multiply both sides of the equation by 4 to get rid of the denominators:
3 * (1/8 - 6y) + 28y = 1/10 * 4
Multiplying through by 4:
3 * (1/8 - 6y) + 28y = 4/10
Now, distribute 3 to (1/8 - 6y):
3/8 - 18y + 28y = 4/10
Combine like terms:
3/8 + 10y = 4/10
To eliminate the fractions, we can multiply both sides by the least common multiple (LCM) of the denominators, which is 40 in this case:
(40 * 3/8) + 40 * 10y = (40 * 4/10)
Multiplying through:
15 + 400y = 16
Now let's isolate y by subtracting 15 from both sides:
400y = 16 - 15
400y = 1
Divide both sides by 400:
y = 1/400
Now that we have the value of y, we can substitute it back into either Equation 1 or Equation 2 to find the value of x. Let's substitute it into Equation 1:
4x + 6(1/400) = 1/8
Multiply through by 400 to remove the fraction:
1600x + 6 = 50
Subtract 6 from both sides:
1600x = 50 - 6
1600x = 44
Divide both sides by 1600:
x = 44/1600
x = 11/400
Therefore, the solution to the system of equations is x = 11/400 and y = 1/400.