Question

Describe the solutions for an equation with two variables of the form Ax+By=C

Answer 1

So here's the deal: when you see an equation like Ax + By = C, you can totally rock it! Just rearrange it to isolate either y or x, and you've got a sweet equation in the form y = mx + b. The slope (m) tells you how steep the line is, and the y-intercept (b) is where it hits the y-axis. Plot some points, connect the dots, and boom! You've got a slick graph that represents the equation. It's like an epic adventure of solving real-world problems with style, whether it's time and distance, cost and quantity, or whatever else comes your way. You got this!

Explanation:

Answer 2

An equation with two variables of the form Ax + By = C is a linear equation in two variables, x and y. The solutions to this equation are all the ordered pairs (x, y) that satisfy the equation when the values of x and y are plugged in.

Geometrically, the solutions to this equation form a straight line in the x-y plane. The slope of the line is -A/B, and the y-intercept is C/B. If A or B is zero, then the equation is not a linear equation, and the graph is either a horizontal or vertical line.

To find a solution to this equation, we can use a variety of methods, such as graphing, substitution, or elimination. Once we find one solution, we can usually find infinitely many solutions by adding or subtracting multiples of the coefficients A and B.

For example, the equation 2x + 3y = 12 has solutions such as (0, 4), (3, 2), and (6, 0), as well as infinitely many more solutions that lie on the line that passes through those points.

Hope this helps!