Good afternoon class! Today, we are going to learn about solving systems of linear equations. There are many ways to solve systems of equations, such as by graphing, or by using the substitution or elimination methods.
To solve a system of equations by graphing, all you have to do is graph each equation. If the problems are not already set to equal the variable y, then you must set them to this first. Then, after graphing them, you must look for the point of intersection between the two equations. This is your answer.
Substitution works by first taking one of the two equations and solving it for either x or y. Let’s just say you were to solve it for y. Then, in the second equation, you would plug in whatever you got in the first equation for y. So, if the first equation was y = 3x - 5 and the second equation was 2x - 2y = 6, you would make the second equation into 2x - 6x + 10 = 6, once you multiply the 2 by the first equation. Then, you would solve this equation for x, to get 1. Using x = 1, you would plug this back into the first equation to find that y = -1. This means that your answer is (1, - 1).
Finally, to use the elimination method, you must first take each equation, and make either the coefficient of x or the coefficient of y in each equation equal to one another. So, as an example, if I was to take the equations 2x + 3y = 5 and 3x + 4y = 7, I would multiply the first equation by 3 and the second equation by 2, so that the coefficients of the x variable are both equal to 6. Then, I would take 6x + 9y = 15 and subtract it by 6x + 8y = 14, to get y = 1. Then using y = 1, I would plug this back into the first equation of 2x + 3y = 5 to get that x = 1. This means that the answer to this system of equations is (1, 1).
Alright everyone, there's the bell. Remember to do this homework that I'm passing out! It's due tomorrow!
I am so confused! I didn't understand anything from that lesson! I just want to give up!
Hey Dave, before you go, I noticed that you seemed a bit overwhelmed as I was going over the lesson. Since you have to get home, I cannot help you right now, but I can give you some advice. Please just try to stay a bit disciplined, and instead of getting overwhelmed straight away, try to first learn the content. Perhaps you could use self-regulation, rather than just letting your emotions get the best of you.
Alright Mrs. Carter, I'll try my best. Thanks for the advice.