Math Problem Statement

Find an ordered pair (x, y) that is a solution to 4x - y = 5.

Solution

The problem in the image is asking for an ordered pair (x,y)(x, y) that satisfies the equation:

4xy=54x - y = 5

To find a solution, we need to assign a value to xx, then solve for yy. Let's choose x=1x = 1 as an arbitrary value for xx, then substitute it into the equation to find yy.

Substitute x=1x = 1 into the equation:

4(1)y=54(1) - y = 5

This simplifies to:

4y=54 - y = 5

Now, solve for yy:

y=54-y = 5 - 4 y=1-y = 1 y=1y = -1

Thus, one solution to the equation is the ordered pair (1,1)(1, -1).

The ordered pair is:

(x,y)=(1,1)(x, y) = (1, -1)

Would you like more details or further explanation?

Here are some related questions for practice:

  1. Find another solution for 4xy=54x - y = 5 by choosing a different value for xx.
  2. Solve for yy in terms of xx for the equation 4xy=54x - y = 5.
  3. What is the general solution for xx and yy if the equation is 2x+y=72x + y = 7?
  4. If y=0y = 0, what is the value of xx in the equation 4xy=54x - y = 5?
  5. How would you check if the ordered pair (2,3)(2, 3) is a solution to 4xy=54x - y = 5?

Tip: Always verify your solution by substituting the values of xx and yy back into the original equation!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

4x - y = 5

Theorems

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Suitable Grade Level

Grades 6-8