Write An Equation To Solve For \[$x\$\] And An Equation To Solve For \[$y\$\]. Choose The Correct Answer Below.A. \($26 + X + 43 = 90$\) And \($118 - Y = 180$\)B. \[$x + 43 = 90$\$\] And \($26 +

by ADMIN 196 views

Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving two equations, one for x and one for y. We will provide step-by-step solutions to these equations and explain the concepts behind them.

Equation 1: Solving for x

The first equation is: 26+x+43=9026 + x + 43 = 90

To solve for x, we need to isolate the variable x on one side of the equation. We can do this by subtracting 26 and 43 from both sides of the equation.

Step 1: Subtract 26 from both sides

26+x+43=9026 + x + 43 = 90

Subtracting 26 from both sides gives us:

x+43=64x + 43 = 64

Step 2: Subtract 43 from both sides

Now, we need to subtract 43 from both sides to isolate x.

x+43=64x + 43 = 64

Subtracting 43 from both sides gives us:

x=21x = 21

Therefore, the value of x is 21.

Equation 2: Solving for y

The second equation is: 118−y=180118 - y = 180

To solve for y, we need to isolate the variable y on one side of the equation. We can do this by subtracting 118 from both sides of the equation.

Step 1: Subtract 118 from both sides

118−y=180118 - y = 180

Subtracting 118 from both sides gives us:

−y=62-y = 62

Step 2: Multiply both sides by -1

Now, we need to multiply both sides by -1 to isolate y.

−y=62-y = 62

Multiplying both sides by -1 gives us:

y=−62y = -62

Therefore, the value of y is -62.

Conclusion

In this article, we solved two equations, one for x and one for y. We provided step-by-step solutions to these equations and explained the concepts behind them. By following these steps, you can solve similar equations and find the value of unknown variables.

Choosing the Correct Answer

Based on our solutions, we can choose the correct answer from the options provided.

A. 26+x+43=9026 + x + 43 = 90 and 118−y=180118 - y = 180

B. x+43=90x + 43 = 90 and 26+y=18026 + y = 180

The correct answer is A. 26+x+43=9026 + x + 43 = 90 and 118−y=180118 - y = 180. This is because our solutions for x and y match the equations provided in option A.

Final Thoughts

Introduction

In our previous article, we solved two equations, one for x and one for y. We provided step-by-step solutions to these equations and explained the concepts behind them. In this article, we will answer some frequently asked questions (FAQs) related to solving equations for x and y.

Q&A

Q: What is the first step in solving an equation for x or y?

A: The first step in solving an equation for x or y is to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: How do I know which operation to perform first?

A: To determine which operation to perform first, you need to look at the equation and identify the variable you want to isolate. Then, you need to determine which operation will help you isolate the variable. For example, if you want to isolate x and the equation is x + 3 = 7, you can subtract 3 from both sides to isolate x.

Q: What is the difference between an equation and an expression?

A: An equation is a statement that says two expressions are equal. For example, 2x + 3 = 5 is an equation. An expression, on the other hand, is a group of numbers and variables combined using mathematical operations. For example, 2x + 3 is an expression.

Q: How do I solve an equation with fractions?

A: To solve an equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. For example, if the equation is 1/2x = 3, you can multiply both sides by 2 to eliminate the fraction.

Q: What is the order of operations when solving an equation?

A: The order of operations when solving an equation is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to solve an equation?

A: Yes, you can use a calculator to solve an equation. However, it's always a good idea to check your work by plugging the solution back into the original equation to make sure it's true.

Q: What if I get stuck while solving an equation?

A: If you get stuck while solving an equation, don't be afraid to ask for help. You can ask a teacher, tutor, or classmate for assistance. You can also try breaking down the equation into smaller steps or using a different approach to solve it.

Conclusion

Solving equations for x and y is an essential skill in mathematics that helps us find the value of unknown variables. By following the steps outlined in this article and answering the FAQs, you can become proficient in solving equations and tackle more complex problems with confidence.

Additional Resources

  • Khan Academy: Solving Equations
  • Mathway: Solving Equations
  • IXL: Solving Equations

Final Thoughts

Solving equations is a skill that takes practice to develop. With patience, persistence, and the right resources, you can become proficient in solving equations and achieve your math goals.