Math Problem Statement

Solve this problem

Solution

The problem visible in the image is:

Given the system of equations:

y=35x+57y = \frac{3}{5}x + \frac{5}{7}

and

n=2x+yn = 2x + y

To solve for nn, we can substitute the expression for yy from the first equation into the second equation.

Step 1: Substitute the value of yy

Substitute y=35x+57y = \frac{3}{5}x + \frac{5}{7} into n=2x+yn = 2x + y:

n=2x+(35x+57)n = 2x + \left(\frac{3}{5}x + \frac{5}{7}\right)

Step 2: Combine like terms

Now, combine the terms involving xx:

n=2x+35x+57n = 2x + \frac{3}{5}x + \frac{5}{7}

To add 2x2x and 35x\frac{3}{5}x, convert 2x2x to a fraction with the same denominator:

2x=105x2x = \frac{10}{5}x

So,

n=105x+35x+57n = \frac{10}{5}x + \frac{3}{5}x + \frac{5}{7}

n=135x+57n = \frac{13}{5}x + \frac{5}{7}

Final Expression for nn

The value of nn in terms of xx is:

n=135x+57n = \frac{13}{5}x + \frac{5}{7}

Would you like to dive into more details or explore specific questions related to this solution?

Here are some related questions you might consider:

  1. What is the value of nn if x=1x = 1?
  2. How do you convert mixed fractions in such equations?
  3. Can we simplify the expression for nn further?
  4. How would the expression for nn change if the coefficients were different?
  5. What are the implications of the different fractions when graphing these equations?

Tip: When solving systems of equations, always try to substitute one variable from one equation into the other to simplify the problem.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Systems of Equations
Linear Equations

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-12