Solution for Pair of Equations 1/16x + 1/15y = 9/20

To solve the given pair of equations, we need to find the values of x and y that satisfy both equations simultaneously.

Step 1: Convert Fractions to a Common Denominator

To make the given equations easier to work with, we can convert the fractions to a common denominator. The smallest common multiple of 16 and 15 is 240, so we can rewrite the equations as:

15/240x + 16/240y = 9/20

Step 2: Simplify the Equations

To simplify the equations, we can multiply both sides by 240 to eliminate the denominators:

15x + 16y = 216

Step 3: Solve for one Variable

To solve for one of the variables, we can choose either x or y and isolate it on one side of the equation. Let's solve for y:

16y = 216 - 15x

y = (216 - 15x)/16

Step 4: Substitute the Solution

Now that we have solved for y in terms of x, we can substitute this expression into one of the original equations to solve for x. Let's use the first equation:

1/16x + 1/15y = 9/20

1/16x + 1/15((216 - 15x)/16) = 9/20

Step 5: Solve for x

Multiplying both sides by 240 to eliminate the denominators, we get:

15x + 16(216 - 15x)/16 = 216

Simplifying the equation, we get:

15x + 216 - 15x = 216

0 = 0

Step 6: Interpret the Result

Since 0 = 0 is a true statement, this means that any value of x will satisfy the given equations. However, we can still solve for y using the expression we found earlier:

y = (216 - 15x)/16

So the solution to the given pair of equations is:

x = any value

y = (216 - 15x)/16