In Exercises 5–18, solve each system by the substitution method.5...

Question

In Exercises 5–18, solve each system by the substitution method.5x + 2y = 0x - 3y = 0

Two linear equations for a system: 5x + 2y = 0 and x - 3y = 0.

Accepted Answer

Hey everyone welcome back in this problem. We are asked to use the substitution method. Okay to solve the system and the system we're given is 10 X plus three, Y equals zero and X minus four, Y equals zero. Okay, so let's go ahead and rewrite what were given 10 X plus three? Y equal zero. Okay. We're going to label these equations. So this will be equation one and equation two is going to be X minus four. Y equals zero. Okay. It's good practice to label them so that when you're referring to them later it's easier and clearer. Alright. So we're told to use the substitution method and the first thing we want to do with the substitution method is we want to isolate one of the variables and one of the equations. Okay so we can choose either equation one or two. We can choose either variable X. Or Y. We're gonna isolate. Now in this case it looks like this X. In the second equation is going to be the easiest to isolate. So let's go ahead and choose that. So working with equation too, we have X minus four Y equals zero. And if we move the four Y to the other side, we're going to get X. Is equal to four. Why? Okay. We're gonna call this equation to star. It's the exact same as equation to same equation. It has the same information. It's just been rearranged to make it easier for us to use. Okay. Alright. So now what we wanna do is we've used equation to to find X equals four Y. We want to set this into the other equation. Okay so that we're finding a solution to both equations. Okay. So we're gonna sub two star into equation one. Alright. So equation one says 10 times X. Which now is four Y. So 10 times four Y plus three Y equals zero. All right, let's expand. We get 40 Y plus three Y equals zero 43 Y equals zero. Well this tells us that why is equal to zero? Okay. Alright. So we found a Y value here. Now we need to go ahead and find the corresponding X. Value. Okay so we're looking for a solution, we're looking for a point. So we need the X. Value. Okay so we're gonna substitute this Y equals zero. Now back into one of our original equations. And we can use either equation. Okay, we can substitute it into equation one or equation to. I'm gonna choose to substitute it into two star. Okay So it's the same as equation too, but we've already rearranged it so we won't need to do that again. Okay so let's substitute Y equals zero Into Equation two star. What we're going to get is X. Is equal to four times Y. In this case is zero. So X is also going to be equal to zero. So we have the point now 00. Okay. And so our solution set is just going to be that zero. This is going to correspond with answer d. Thanks everyone for watching See you in the next video.

In Exercises 5–18, solve each system by the substitution method.5x + 2y = 0x - 3y = 0

Key Concepts

Systems of Linear Equations

Substitution Method

Graphical Interpretation

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