This week in Math 10, the concept that I chose as the most important thing I have learned is finding the solution of two lines. I chose this because prior to this week I didn’t know anything about what a solution of two lines meant, so it is new to me and it is an important part of understanding systems of linear equations because it shows how two lines are connected. Systems of linear equations are sets of equations that you work with at the same time, and the solution of these systems is the point where the lines cross on the graph. A solution of one line is any ordered pair that is a point that the line goes through, meaning that when you put those values into the linear equation, both sides of the equation will result in equal values, meaning that the coordinate is a solution to the equation. The solution of two lines is the one point on the graph with the coordinates that are a solution for each of the linear equations of the different lines.

How to find the solution of two lines:

Step 1: To find the solution of two lines when given linear equations, you first plot the lines on the same graph to be able to see where the lines intercept.

Step 2: Look at the point where the lines cross. The coordinate of that point is the solution.

Step 3: Check that the solution is correct by inputting the x and y value of the ordered pair into the linear equation and solving each side to assure that it results in the same number.

Example:

y = 2x +3

y = -3x -7

Solution: (-2,-1)

This is the solution because it is the point where the lines cross on the graph.

 

 

Checking the solution of this example:

First take the linear equation:

y = 2x +3

Then replace x and y with the x and y values in the solution and see if the sides are equal:

-1 = 2(-2) +3

-1 = -4+3

-1 = -1

Check for each linear equation in the system:

y = -3x -7

-1 = -3(-2) -7

-1 = 6 -7

-1 = -1