Math Problem Statement

2x+5y=15

Solution

The equation 2x+5y=152x + 5y = 15 represents a linear equation in two variables. There are various ways to approach or analyze this equation, depending on what you want to do with it. Here are a few possibilities:

1. Solving for one variable in terms of the other:

You can express one variable in terms of the other. For instance, solve for yy in terms of xx: 5y=152x5y = 15 - 2x y=152x5y = \frac{15 - 2x}{5} Or solve for xx in terms of yy: 2x=155y2x = 15 - 5y x=155y2x = \frac{15 - 5y}{2}

2. Finding intercepts:

  • x-intercept: Set y=0y = 0, then solve for xx: 2x=15x=1522x = 15 \quad \Rightarrow \quad x = \frac{15}{2} So, the x-intercept is (152,0)\left( \frac{15}{2}, 0 \right).

  • y-intercept: Set x=0x = 0, then solve for yy: 5y=15y=35y = 15 \quad \Rightarrow \quad y = 3 So, the y-intercept is (0,3)(0, 3).

3. Graphing the equation:

You can plot the equation by finding two points (like the intercepts) and then drawing a line through them.

4. Slope-intercept form:

The equation can be rewritten in slope-intercept form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept: y=25x+3y = -\frac{2}{5}x + 3 Here, the slope m=25m = -\frac{2}{5} and the y-intercept is 33.

5. Standard form:

This equation is already in standard form Ax+By=CAx + By = C, where A=2A = 2, B=5B = 5, and C=15C = 15.


Do you want more details on any of these methods, or have any other questions?

Here are 5 related questions:

  1. How can we solve this system if we add another equation?
  2. How do you determine the slope of a line from its equation?
  3. How can we graph this linear equation step by step?
  4. Can we find a specific solution for xx and yy given additional constraints?
  5. What real-world situations can this equation represent?

Tip: In linear equations, the slope tells you how steep the line is, while the intercepts show where the line crosses the axes.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra

Formulas

2x + 5y = 15
y = (15 - 2x) / 5
x = (15 - 5y) / 2
Slope-Intercept Form: y = mx + b
Standard Form: Ax + By = C

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 6-9