Find the value of (x/y)^2 given x + y = 3 and x - y = 9

Published on October 21, 2024

Algebra

By solving the system of equations x + y = 3 and x - y = 9, we find x = 6 and y = -3. Then, substituting these values into (x/y)^2, we get 4.

Question

Answer

We are given the following system of equations:

and we want to find

Step 1: Solve for one variable in terms of the other.

Let’s solve the first equation for

Step 2: Substitute the expression from Step 1 into the second equation.

Substituting

into the second equation gives:

Step 3: Solve for the remaining variable.

Simplifying the equation from Step 2:

Step 4: Substitute the value found in Step 3 back into either of the original equations to solve for the other variable.

Let’s substitute

into the equation

Step 5: Substitute the values of

and

into the expression we want to evaluate.

Substituting

and

into

gives:

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