Solve The Equation X+2y-4=0 And 2x+4y-12=0 Graphically

4 min read Jun 26, 2024
Solve The Equation X+2y-4=0 And 2x+4y-12=0 Graphically

Solving Systems of Linear Equations Graphically

In this article, we will learn how to solve a system of linear equations graphically. Specifically, we will solve the equations:

Equation 1: x + 2y - 4 = 0 Equation 2: 2x + 4y - 12 = 0

What is a System of Linear Equations?

A system of linear equations is a set of two or more linear equations that share variables. In this case, we have two linear equations with two variables, x and y. To solve a system of linear equations, we need to find the values of x and y that satisfy both equations.

How to Solve a System of Linear Equations Graphically

To solve a system of linear equations graphically, we will follow these steps:

  1. Graph each equation on a coordinate plane
  2. Find the point of intersection
  3. Write the solution

Step 1: Graph Each Equation on a Coordinate Plane

Let's start by graphing each equation on a coordinate plane.

Equation 1: x + 2y - 4 = 0

To graph this equation, we can rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

x + 2y - 4 = 0 2y = -x + 4 y = (-1/2)x + 2

Now we can graph the equation:

!

Equation 2: 2x + 4y - 12 = 0

To graph this equation, we can also rewrite it in slope-intercept form:

2x + 4y - 12 = 0 4y = -2x + 12 y = (-1/2)x + 3

Now we can graph the equation:

!

Step 2: Find the Point of Intersection

Next, we need to find the point of intersection between the two graphs. To do this, we can look for the point where the two lines intersect.

!

In this case, the point of intersection is (2, 2).

Step 3: Write the Solution

Finally, we can write the solution to the system of linear equations.

x = 2 y = 2

Therefore, the solution to the system of linear equations is x = 2 and y = 2.

Conclusion

In this article, we learned how to solve a system of linear equations graphically. By graphing each equation on a coordinate plane, finding the point of intersection, and writing the solution, we can solve systems of linear equations and find the values of the variables.

Featured Posts