Find An Ordered Pair \[$(x, Y)\$\] That Is A Solution To The Equation.$\[4x - Y = 7\\]\[$(x, Y) = (\ \ \ \ , \ \ \ \ )\$\]

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Introduction

In mathematics, solving equations is a fundamental concept that helps us understand the relationship between variables. When we are given an equation, our goal is to find the values of the variables that satisfy the equation. In this article, we will focus on finding an ordered pair (x, y) that is a solution to the equation 4x - y = 7.

Understanding the Equation

The given equation is a linear equation in two variables, x and y. The equation is in the form of 4x - y = 7, where 4x represents the coefficient of x, and -y represents the coefficient of y. The constant term is 7.

Coefficients and Constants

Coefficients

The coefficients of x and y are 4 and -1, respectively. The coefficient of x is a positive number, which means that the value of x will increase as the value of the equation increases. On the other hand, the coefficient of y is a negative number, which means that the value of y will decrease as the value of the equation increases.

Constants

The constant term in the equation is 7. This means that when x is equal to 0, the value of y will be 7.

Solving the Equation

To solve the equation 4x - y = 7, we can use the method of substitution or elimination. In this case, we will use the method of substitution.

Substitution Method

Step 1: Isolate y

We can isolate y by adding y to both sides of the equation. This gives us:

4x - y + y = 7 + y

Simplifying the equation, we get:

4x = 7 + y

Step 2: Solve for y

Now, we can solve for y by subtracting 7 from both sides of the equation. This gives us:

4x - 7 = y

Step 3: Find the Value of y

To find the value of y, we need to find the value of x that satisfies the equation. Let's assume that x = 2. Substituting x = 2 into the equation, we get:

4(2) - 7 = y

Simplifying the equation, we get:

8 - 7 = y

y = 1

Finding the Ordered Pair (x, y)

Now that we have found the value of y, we can find the ordered pair (x, y) that is a solution to the equation. The ordered pair is (2, 1).

Conclusion

In this article, we have found an ordered pair (x, y) that is a solution to the equation 4x - y = 7. The ordered pair is (2, 1). We have used the method of substitution to solve the equation and have found the value of y by substituting x = 2 into the equation.

Frequently Asked Questions

Q: What is the equation 4x - y = 7?

A: The equation 4x - y = 7 is a linear equation in two variables, x and y.

Q: How do I solve the equation 4x - y = 7?

A: You can use the method of substitution or elimination to solve the equation.

Q: What is the ordered pair (x, y) that is a solution to the equation 4x - y = 7?

A: The ordered pair (x, y) that is a solution to the equation 4x - y = 7 is (2, 1).

References

  • [1] "Linear Equations in Two Variables" by Math Open Reference
  • [2] "Solving Linear Equations" by Khan Academy

Further Reading

  • "Linear Equations in Two Variables" by Math Open Reference
  • "Solving Linear Equations" by Khan Academy
  • "Algebra" by Michael Artin

Related Topics

  • Linear Equations in Two Variables
  • Solving Linear Equations
  • Algebra

Tags

  • Linear Equations in Two Variables
  • Solving Linear Equations
  • Algebra
  • Mathematics

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Introduction

Linear equations in two variables are a fundamental concept in mathematics that helps us understand the relationship between two variables. In this article, we will answer some frequently asked questions about linear equations in two variables.

Q&A

Q: What is a linear equation in two variables?

A: A linear equation in two variables is an equation that involves two variables, x and y, and is in the form of ax + by = c, where a, b, and c are constants.

Q: How do I solve a linear equation in two variables?

A: You can use the method of substitution or elimination to solve a linear equation in two variables.

Q: What is the difference between the method of substitution and the method of elimination?

A: The method of substitution involves substituting the value of one variable into the other variable, while the method of elimination involves adding or subtracting the two equations to eliminate one variable.

Q: How do I find the value of y in a linear equation in two variables?

A: You can find the value of y by substituting the value of x into the equation and solving for y.

Q: What is the ordered pair (x, y) that is a solution to a linear equation in two variables?

A: The ordered pair (x, y) that is a solution to a linear equation in two variables is a pair of values that satisfy the equation.

Q: How do I graph a linear equation in two variables?

A: You can graph a linear equation in two variables by plotting the points that satisfy the equation and drawing a line through them.

Q: What is the slope of a linear equation in two variables?

A: The slope of a linear equation in two variables is the ratio of the change in y to the change in x.

Q: How do I find the slope of a linear equation in two variables?

A: You can find the slope of a linear equation in two variables by using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Q: What is the y-intercept of a linear equation in two variables?

A: The y-intercept of a linear equation in two variables is the value of y when x is equal to 0.

Q: How do I find the y-intercept of a linear equation in two variables?

A: You can find the y-intercept of a linear equation in two variables by substituting x = 0 into the equation and solving for y.

Conclusion

In this article, we have answered some frequently asked questions about linear equations in two variables. We hope that this article has helped you understand the concept of linear equations in two variables and how to solve them.

Further Reading

  • "Linear Equations in Two Variables" by Math Open Reference
  • "Solving Linear Equations" by Khan Academy
  • "Algebra" by Michael Artin

Related Topics

  • Linear Equations in Two Variables
  • Solving Linear Equations
  • Algebra

Tags

  • Linear Equations in Two Variables
  • Solving Linear Equations
  • Algebra
  • Mathematics

Additional Resources

  • [1] "Linear Equations in Two Variables" by Math Open Reference
  • [2] "Solving Linear Equations" by Khan Academy
  • [3] "Algebra" by Michael Artin

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