The Solution To A System Of Equation

We’re going to solve a few linear equations. So, let’s begin with the systems of equations, how to solve them and also learn how to solve matrices. With this example, x plus 4 is equal to 7. How can we solve this linear equation? The goal here is to calculate the value of x? Here, x is a variable it has a value that we currently don’t know, and x is just basically a number; we just got to find out the value of that number. So now, let’s think about this equation intuitively. How would you get 7 when you have x plus 4 as a linear equation? If you think about it, we know that 3 plus 4 is equal to 7. So, in this equation, x has a value of 3. 

But now, let’s talk about a step-by-step process that will help us to get this answer. In this equation, x is added to 4, and that equals 7. In order to solve the linear equation, what you want to do is you want to get the x variable by itself on one side of the linear equation; the only way to do that is to get rid of the four; what you need to do is perform the opposite operation of what you see here. The opposite of addiction is subtraction. We need to subtract both sides by four. Whatever you do to the left side, you must also do to the right side. Positive 4 plus negative 4 adds up to 0.  They cancel out now; we’re going to bring down the x, and here we have x equal to 3. So that’s how we could solve that particular linear equation.

Now, let’s try out some examples-

Example 1  a) x plus 9 is equal to 15 

b) 6 plus x is equal to 13

a) What number plus 9 is equal to fifteen? We know that six plus nine is fifteen, so therefore x has to equal six. Now to show your work, what you could do is perform the opposite operation of addition, so we see plus nine. Let’s subtract both sides by nine. These two will cancel. We can bring down the x, and so we’ll get x is equal to fifteen minus nine. Fifteen minus nine is six and for those of you who may not be sure of that, what you could do is you could use a number line. Let’s say you have fifteen here; if you want to subtract it by 9, simply travel 9 units to the left, so this is 14 13 12 …7 6. When you’re subtracting, move to the left. Using the number line when you’re adding, just move to the right. That’s how you can do 15 minus 9.

Now let’s work on the next linear equation, so here

b) We have six plus x is thirteen. Six plus what number adds up to thirteen? We know that six plus seven is thirteen. Therefore, x is going to be the number seven. Now let’s show our work. What we need to do in this example is the opposite of plus six. We need to subtract both sides by six so that they will cancel each other. We can bring down the x, and here we have thirteen minus six, which is seven. Hence, we get x is equal to seven.

So that’s how we could solve this step linear equation problems and the system of equations how to solve.

How do we solve a system of linear equations? How to solve using matrices and determinants? So, one f the way is to solve it with the usual techniques that we’ve been using, or we can use matrices to solve them. Yes, matrices!

To solve the equations using matrices and determinants, we first need to write them in the matrix form. So, we first write the matrix of the coefficients. There is the matrix of coefficients of the two variables. And this will be multiplied by the matrix, which has the column of variables. The variables can be X and Y. So, a matrix with the coefficients multiplied with a matrix with a column of variables. And this product is equal to a matrix with a column of the constants on the right-hand side.

Why do we say that this is the matrix form?

We will know why when we multiply these two matrices. Do you remember the multiplication of matrices? To know if two matrices can be multiplied, we need to check their order. The order of this matrix is two by two, two by one and so on. 

Conclusion-

Suppose you are interested in linear equation-based questions. You can try a variety of other types rather than just variables and matrices. I’ll suggest that you should practice more as these types of questions require all the practice in the world so that you can get familiarized with them.