Math Problem Statement

2x + 3y = 5

Solution

The image contains the equation:

2x+3y=52x + 3y = 5

This is a linear equation in two variables xx and yy. If you need to solve for one variable in terms of the other, or to graph it, let me know. Here are a few possible steps:

1. Solve for yy in terms of xx:

3y=52x    y=52x33y = 5 - 2x \implies y = \frac{5 - 2x}{3}

2. Solve for xx in terms of yy:

2x=53y    x=53y22x = 5 - 3y \implies x = \frac{5 - 3y}{2}

3. Find specific solutions if either xx or yy is given.

Would you like to proceed with any of these? Do you have any questions or need further details?

Here are 5 related questions for practice:

  1. What is the slope of the line represented by 2x+3y=52x + 3y = 5?
  2. How do you graph this equation on a Cartesian plane?
  3. What are the x- and y-intercepts of the line 2x+3y=52x + 3y = 5?
  4. How would you write this equation in standard form?
  5. How do you find a solution pair (x,y)(x, y) that satisfies the equation?

Tip: When solving for one variable, always perform operations symmetrically on both sides of the equation to maintain equality.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Standard form of linear equations: ax + by = c
Slope-intercept form: y = mx + b

Theorems

Linear equation properties
Slope of a line
Intercepts of a line

Suitable Grade Level

Grades 7-10