Math Problem Statement

2x - y = 5

Solution

The equation you provided is:

2xy=52x - y = 5

This is a linear equation in two variables, xx and yy. To explore it further, you can:

  1. Solve for yy in terms of xx:

    y=2x5y = 2x - 5

    This is the slope-intercept form, y=mx+by = mx + b, where the slope m=2m = 2 and the y-intercept is 5-5.

  2. Solve for xx in terms of yy**:

    x=y+52x = \frac{y + 5}{2}
  3. Graph the equation: The graph of this equation would be a straight line with a slope of 2 and a y-intercept at 5-5.

  4. Find the intercepts:

    • To find the x-intercept (where y=0y = 0): 2x0=5    x=522x - 0 = 5 \implies x = \frac{5}{2}
    • To find the y-intercept (where x=0x = 0): 2(0)y=5    y=52(0) - y = 5 \implies y = -5

Would you like more details or have any questions on this?

Here are 5 questions to further explore this equation:

  1. How would you graph this equation on a coordinate plane?
  2. What happens to the slope if the equation changes to 2xy=102x - y = 10?
  3. How would you find the solution to this equation if another equation is given?
  4. Can you solve this equation using matrices or determinants?
  5. What is the effect of multiplying both sides of the equation by a constant?

Tip: When solving for a variable, isolating it on one side of the equation helps to make the relationship between variables clear.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Slope-intercept form: y = mx + b
General solution for x: x = (y + 5)/2

Theorems

Linear Equation Theorem
Intercepts of a Line

Suitable Grade Level

Grades 6-8