Solve each system graphically. Check your solutions. Do not use a calculator. x+y=3 2

Solve each system graphically. Check your solutions. Do not...

Key Concepts

System of Linear Equations

This concept involves working with two or more equations containing the same set of variables and finding the values that satisfy all equations simultaneously. It is a fundamental topic in algebra that can be approached using various methods such as substitution, elimination, or graphing.

Graphical Method

Graphing each equation as a line on the coordinate plane is an effective technique to visualize and solve a system of linear equations. By plotting the equations, the solution to the system is given by the point where the lines intersect, making it easier to understand the behavior of the system and verify the solution without relying on calculators.

Intersection Point

The intersection point of the graphs of equations in a system represents the set of variable values that satisfy all the equations concurrently. It is a crucial concept as it visually confirms the solution to the system of equations, validating the accuracy of the method used to solve the problem.

Transcript

00:01 According to the question, we have to solve the system of linear equations graphically.

00:06 So the equations are x plus y equals 3.

00:10 This is our first equation and the second equation is 2x minus y equals 0.

00:16 So how should we proceed? that first, in order to sketch the graph of the first equation, we are going to find the x intercept and y intercept of the straight line.

00:30 So this can be done in, so the given equation is x plus y equals 3.

00:35 So if you divide both sides of the equation by 3, then it will become x upon 3 plus y upon 3 equals 1.

00:43 So from here we can say that the x intercept will be equals 3 and the y intercept will be equal 3.

00:50 So we got two points which satisfies the straight line, given straight line and they are 3 .0 and 0 .3.

00:56 So here we have 3 .0 and here we have 0 .3 and with the help of these two points we can sketch the graph of the given straight line now we have to sketch the graph of the straight line 2x minus y equals 0 so 2x minus y equals 0 can be written as y equals 2x so from here we can say that since the straight line satisfies the point 0 .0 that is when x equals 0 then y will also become 0 so it will pass through the origin so the x intercept and y intercept both will be equal 0 right okay but we only got one point in order in order to sketch the graph of the straight line we need another point which satisfies the equation of the straight line so suppose we put a point 2 so when x equals 2 y equals 4 because 2 multiplied by 2 equals 4 so 2 comma 4 is another point which satisfies the given straight line so we got 2 points which satisfies the given straight line 1 is 0 .0 and another 1 is 2 so here we have 2 .4 and since we have got the two points we can simply sketch the graph of the straight line and once we have sketched both the graphs then we can get the intersection point and the intersection point is 1 .2...

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