Use The Equation Below And The Indicated Value To Find An Ordered Pair That Is A Solution.${ Y = 4x - 3 }$Let ${ X = 2 }$The Ordered Pair Is { (2, \square)$}$.(Simplify Your Answer. Type An Integer Or A Fraction.)

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Introduction

In mathematics, solving linear equations is a fundamental concept that helps us find the value of unknown variables. When we are given a linear equation and a value for one of the variables, we can use this information to find the corresponding value of the other variable. In this article, we will explore how to use the equation y = 4x - 3 and the value x = 2 to find an ordered pair that is a solution.

Understanding Linear Equations

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable. Linear equations can be solved using various methods, including substitution, elimination, and graphing.

The Equation y = 4x - 3

The equation y = 4x - 3 is a linear equation in which the variable y is expressed in terms of the variable x. The coefficient of x is 4, and the constant term is -3. This equation represents a straight line with a slope of 4 and a y-intercept of -3.

Substituting x = 2 into the Equation

Now that we have the equation y = 4x - 3, we can substitute the value x = 2 into the equation to find the corresponding value of y. To do this, we simply replace x with 2 in the equation:

y = 4(2) - 3

Simplifying the Equation

To simplify the equation, we can multiply 4 and 2 to get 8, and then subtract 3:

y = 8 - 3

y = 5

The Ordered Pair

Now that we have found the value of y, we can write the ordered pair as (2, 5). This means that when x = 2, the corresponding value of y is 5.

Conclusion

In this article, we used the equation y = 4x - 3 and the value x = 2 to find an ordered pair that is a solution. We substituted the value of x into the equation, simplified the resulting expression, and found the value of y. The ordered pair is (2, 5), which means that when x = 2, the corresponding value of y is 5.

Example Problems

Here are a few example problems that you can try to practice solving linear equations:

  • y = 2x + 1, x = 3
  • y = x - 2, x = 5
  • y = 3x - 1, x = 2

Tips and Tricks

Here are a few tips and tricks that can help you solve linear equations:

  • Make sure to substitute the value of the variable into the equation correctly.
  • Simplify the resulting expression by combining like terms.
  • Check your answer by plugging it back into the original equation.

Real-World Applications

Linear equations have many real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

In conclusion, solving linear equations is an important concept in mathematics that has many real-world applications. By understanding how to substitute values into equations and simplify resulting expressions, we can find ordered pairs that are solutions to linear equations. With practice and patience, you can become proficient in solving linear equations and apply this knowledge to real-world problems.

Introduction

In our previous article, we explored how to use the equation y = 4x - 3 and the value x = 2 to find an ordered pair that is a solution. In this article, we will answer some frequently asked questions about solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you can use the following steps:

  1. Substitute the value of the variable: Substitute the value of the variable into the equation.
  2. Simplify the resulting expression: Simplify the resulting expression by combining like terms.
  3. Check your answer: Check your answer by plugging it back into the original equation.

Q: What is an ordered pair?

A: An ordered pair is a pair of values that correspond to each other. In the context of linear equations, an ordered pair is a pair of values that satisfy the equation.

Q: How do I find an ordered pair that is a solution to a linear equation?

A: To find an ordered pair that is a solution to a linear equation, you can use the following steps:

  1. Substitute the value of the variable: Substitute the value of the variable into the equation.
  2. Simplify the resulting expression: Simplify the resulting expression by combining like terms.
  3. Write the ordered pair: Write the ordered pair as (x, y), where x is the value of the variable and y is the corresponding value.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

  • Not simplifying the resulting expression: Make sure to simplify the resulting expression by combining like terms.
  • Not checking your answer: Make sure to check your answer by plugging it back into the original equation.
  • Not using the correct order of operations: Make sure to use the correct order of operations when simplifying the resulting expression.

Q: How do I apply linear equations to real-world problems?

A: Linear equations can be applied to a wide range of real-world problems, including:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Q: What are some tips and tricks for solving linear equations?

A: Some tips and tricks for solving linear equations include:

  • Make sure to substitute the value of the variable into the equation correctly.
  • Simplify the resulting expression by combining like terms.
  • Check your answer by plugging it back into the original equation.

Conclusion

In conclusion, solving linear equations is an important concept in mathematics that has many real-world applications. By understanding how to substitute values into equations and simplify resulting expressions, we can find ordered pairs that are solutions to linear equations. With practice and patience, you can become proficient in solving linear equations and apply this knowledge to real-world problems.

Example Problems

Here are a few example problems that you can try to practice solving linear equations:

  • y = 2x + 1, x = 3
  • y = x - 2, x = 5
  • y = 3x - 1, x = 2

Practice Exercises

Here are a few practice exercises that you can try to practice solving linear equations:

  • Solve the equation y = 2x + 3 when x = 4.
  • Solve the equation y = x - 1 when x = 6.
  • Solve the equation y = 3x - 2 when x = 5.

Real-World Applications

Linear equations have many real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

In conclusion, solving linear equations is an important concept in mathematics that has many real-world applications. By understanding how to substitute values into equations and simplify resulting expressions, we can find ordered pairs that are solutions to linear equations. With practice and patience, you can become proficient in solving linear equations and apply this knowledge to real-world problems.