how to solve this??
13y=10
x+Y+Z=39
16x=13z
from the first: y = 10/13
from the last: z = 16/13x
into the second:
x + 10/13 + 16/13x = 39
times 13
13x + 10 + 16x = 507
29x = 497
x = 497/29
now I can find z = (16/13(497/29) = 7952/377
x = 497/13 , y = 10/13 , z = 7952/377
weird!
To solve the system of equations given, we will use principles of algebra to find the values of variables y, x, and z.
First Equation:
To solve the equation 13y = 10, divide both sides of the equation by 13. This will isolate the variable y and give you its value.
13y / 13 = 10 / 13
y = 10 / 13
Second Equation:
To solve the equation x + y + z = 39, we need more information about the values of variables x and z. As it is, we can't solve for x and z with only this equation.
Third Equation:
To solve the equation 16x = 13z, we can rewrite it in terms of either x or z to find their relationship.
Divide both sides of the equation by 16.
16x / 16 = 13z / 16
x = 13z / 16
Now, let's substitute the value of x in the second equation with 13z / 16:
(13z / 16) + y + z = 39
We also have the value of y from the first equation: y = 10 / 13
Substituting these values in the second equation:
(13z / 16) + (10 / 13) + z = 39
Now, we can solve this equation to find the value of z.
Multiply both sides of the equation by the least common denominator (LCD), which is 16 * 13 = 208 to eliminate fractions:
(13z * 208 / 16) + (10 * 208 / 13) + z * 208 = 39 * 208
Simplify the equation:
1352z + 1600 + 208z = 8112
Combine like terms:
1560z + 1600 = 8112
Subtract 1600 from both sides:
1560z = 6512
Divide both sides by 1560:
z = 6512 / 1560
Simplify the fraction:
z ≈ 4.18
Now, substitute the value of z back into the equation we found for x:
x = 13z / 16
x = 13 * 4.18 / 16
x ≈ 3.38
Finally, substitute the values of x and z into the second equation:
3.38 + y + 4.18 = 39
Combine the terms:
y + 7.56 = 39
Subtract 7.56 from both sides:
y = 39 - 7.56
y ≈ 31.44
So, the solution to the system of equations is:
x ≈ 3.38, y ≈ 31.44, and z ≈ 4.18.