Linear Equations: Understanding 10x + 15y
In algebra, linear equations are a fundamental concept in mathematics. They are equations in which the highest power of the variable(s) is 1. In this article, we will explore the linear equation 10x + 15y and learn how to solve it.
What is 10x + 15y?
The equation 10x + 15y is a linear equation in two variables, x and y. It is a simple equation that represents a straight line on a coordinate plane. The equation is in the form of Ax + By = C, where A, B, and C are constants.
Graphing 10x + 15y
To graph the equation 10x + 15y, we can use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. However, in this case, we need to rewrite the equation in the slope-intercept form.
Let's solve for y:
10x + 15y = 0
Subtract 10x from both sides:
15y = -10x
Divide both sides by 15:
y = (-10/15)x
y = (-2/3)x
So, the slope (m) is -2/3, and the y-intercept (b) is 0.
Now, we can graph the equation on a coordinate plane.
Solving 10x + 15y
To solve the equation 10x + 15y, we need to find the values of x and y that satisfy the equation. There are infinitely many solutions, as the equation represents a straight line.
One way to solve the equation is to use substitution or elimination methods. Let's use the substitution method.
Assume x = 3. Then, substitute x into the equation:
10(3) + 15y = 0
30 + 15y = 0
Subtract 30 from both sides:
15y = -30
Divide both sides by 15:
y = -2
So, one solution is x = 3, y = -2.
Conclusion
In this article, we have explored the linear equation 10x + 15y. We have learned how to graph the equation and solve it using the substitution method. Linear equations are an essential concept in algebra, and understanding them is crucial for more advanced math topics.
