Week 17 of Math 10 and Week 7  of cautious online classes. We are now learning a new topic which is the called the System of Linear Equations. In this blog post I will be covering what it is and how to solve for it without the use of graphs.

A system is essentially a set of linear equations that work together, and is described through two equations that can be written into lines. The point at which the two lines cross is called the solution of the system, which is a specific coordinate and the only coordinate where both lines intersect. For example, if we had 2x+y=4 and 3x+y=6 as our two equations, the solution would be the coordinate (2,0).

In order for us to confirm that this indeed is the solution we have to plug the numbers from the coordinate into their respective variable. If we do that we get 2(2)+0=4 which is true, and 3(2)+0=6 which is also true. If both equations result in a “true” statement then the solution is correct.

However, we while it was easy for us to insert the number into a graphing calculator like Desmos, we should also be able to know how to  solve for the solution algebraically. So let’s try to solve a new question without the use of a graph. This time our two equations are 5x-3y=27 and 2x+y=2. First, we start off by choosing an equation, then isolating either x or y. We can start off by doing equation 2 with the intent of isolating y.

Now that we know the value of y, we can plug in the y value into equation 2.

Now that we know what the x value is, we can go backwards and plug it into the previous equation to find the actual value of y.

So now we know that x=3 and y=-4, therefore the solution is (3,-4). Finally, you would want to double check if the solution is actually correct by inserting them into the initial first two equations to see if they’re true.

And you’re done!

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