Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of sin x° and cos y° share? A right triangle is shown with one leg measuring 8 and another leg measuring 6. The angle across from the leg measuring 6 is marked x degrees, and the angle across from the leg measuring 8 is marked y degrees.

10 hours at job (1)

2 hours at job (2)

Step-by-step explanation:

As per the given information, one earns ($8) dollars at one of their jobs, and ($10) hours at the other. One must earn a total of ($100) dollars, and can work no more than (12) hours. Let (x) be the hours worked at job 1 and (y) be the hours worked at job two.

Since one can work no more than (12) hours, the sum of (x) and (y) must be (12), therefore the following equation can be formed;

One earns ($8) dollars at one of their jobs and ($10) at the other, but one earns a total of (100) one can form an equation to represent this situation.  Multiply the hours worked by the money earn per hour for each job, add up the result and set it equal to (100).

Now set up these equations in a system;

Use the process of elimination to solve this system. The process of elimination is a method of solving a system of equations. One must first manipulate one of the equations in the system such that one of the variable coefficients is the additive inverse of the other. That way, when one adds the equation, the variable cancels, one can solve for the other variable then back solve to find the value of the first variable,

Manipulate,

Simplify,

Add,

Inverse operations,

Backsolve for (x), use equation one to achieve this,

Substitute,

Inverse operations,