Math Problem Statement

The equation x = 2y - 1 is substituted into y = x + 20. Which of the following is the correct equation resulting from the substitution?

Solution

Let's solve this step by step.

You are given two equations:

  1. x=2y1x = 2y - 1
  2. y=x+20y = x + 20

You need to substitute the first equation into the second.

Step 1: Substitute x=2y1x = 2y - 1 into y=x+20y = x + 20.

y=(2y1)+20y = (2y - 1) + 20

Step 2: Simplify the equation.

y=2y1+20y = 2y - 1 + 20 y=2y+19y = 2y + 19

Step 3: Solve for yy.

Subtract 2y2y from both sides:

y2y=19y - 2y = 19

y=19-y = 19

Multiply both sides by -1:

y=19y = -19

Conclusion:

The correct equation resulting from the substitution is y=19y = -19.

So the correct answer is D.


Do you want more details on this solution or have any questions?

Here are some related questions for further practice:

  1. How would you solve for xx after finding y=19y = -19?
  2. What happens if the equation y=x+20y = x + 20 is substituted into another equation?
  3. Can you graph both equations x=2y1x = 2y - 1 and y=x+20y = x + 20 and find their intersection point?
  4. How would the solution change if the equation was x=2y+1x = 2y + 1 instead of x=2y1x = 2y - 1?
  5. How would you approach solving the system if both equations were quadratic instead of linear?

Tip: Always check your final answer by substituting it back into the original equations to verify correctness.

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Math Problem Analysis

Mathematical Concepts

Algebra
Substitution Method
Linear Equations

Formulas

y = x + 20
x = 2y - 1

Theorems

Substitution in linear equations

Suitable Grade Level

Grades 9-10