Solve each system by graphing. See Example 2. x+y=4 2 x-y=2

Name: Problem 17, Chapter 4: Intermediate Algebra
Uploaded: 2020-07-29T10:22:30-08:00
Duration: 6 min 8 s
Channel: Supratim Roy
Description: Solve each system by graphing. See Example 2. x+y=4 2 x-y=2

Solve each system by graphing. See Example 2. x+y=4 ...

Key Concepts

Systems of Linear Equations

This concept involves dealing with two or more linear equations that share the same set of variables. The solution to the system is the set of variable values that satisfy all equations simultaneously. Understanding systems of linear equations is fundamental in algebra as it provides methods to solve problems involving multiple constraints.

Graphing Method

The graphing method is a visual approach for solving systems of equations by plotting each equation on the same coordinate plane as straight lines. This method allows one to find the solution by identifying the point where the lines intersect, which represents the common solution to all equations in the system.

Intersection of Lines

In the context of solving systems by graphing, the intersection point of two lines represents the solution where both equations are satisfied. This intersection is crucial because it provides a concrete method for visual verification of the solution, especially in cases where the system is consistent and has exactly one solution.

Transcript

0:00 Hello everyone.

00:01 So here we have a system of linear equations in two variables and we have to solve them by graphing.

00:10 Okay.

00:11 So let us find the coordinates of each equations to make straight lines on the graph.

00:19 Okay.

00:19 So we need two coordinates for each equation.

00:22 Okay.

00:23 So i have made two boxes to write down the coordinates.

00:26 So the first one is for the equation one and the second one is for the second equation.

00:30 Okay so let me just put the values and check for the values of x and y okay so if it is for the first equation if i take x as a one okay so what would be y so we can write one plus y equals 4 which implies y equals 4 minus 1 which is equals to 3 so the value of y is 3 so similarly if i take x as a 2 so 2 plus y equals 4 which implies y equals 4 minus 2 equals to 2 so we have y equals to 2 okay fine so we have found the coordinates for the first equation okay so now let us do for the second one okay so if i take x as one over here okay so if i take x1 so let us see what is y okay so 2 multiplied by 1 will be 2 2 minus y equals 2 okay so which implies minus y equals 0 okay and y equals 0 so for 2 or 1 it is 0 now again let us take x as 0 okay so here if we take x 0 so what would happen we will have only negative y so negative y would be equal to 2 so this for x equals to 0 so y will be equal to negative 2 okay so we have our table for the coordinates.

02:44 Now we will make the graph.

02:50 So the first equation, the line i will represent it by red.

02:55 Okay...

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