Problem 100 - Introductory Algebra for College Students

Question

Explain how to find ordered pairs that are solutions of an equation in two variables, \(x\) and \(y\)

Step-by-Step Solution

Answer

To find the ordered pairs which are solutions of an equation in two variables, choose a value for one variable, substitute it into the equation, solve for the other variable and write down your results as an ordered pair (x, y). Repeat this process with different values to obtain more ordered pairs.

Step 1: Choose a variable to substitute

Choose either \(x\) or \(y\) to substitute with a specific value. This could be a random choice, or it may be determined by the specifics of the equation that needs to be solved.

Step 2: Substitute and Solve

Substitute the chosen value into the equation and solve for the remaining variable.

Step 3: Write the Ordered Pair

After the calculations, an ordered pair can be written. The first number in the pair is the substituted value of \(x\) and the second one is the calculated value of \(y\)