In Exercises 19–30, solve each system by the addition method. ...

Question

In Exercises 19–30, solve each system by the addition method. x + 2y = 2 - 4x + 3y = 25

Exercise 23: Solve the system of equations x + 2y = 2 and -4x + 3y = 25 using the addition method.

Accepted Answer

Hey everyone welcome back in this problem. We are asked to consider the given system of equations and solve using the addition method. And the equations were given are three X plus eight. Y equals two and x minus three Y equals to a system of two equations. Let's go ahead and just label the equation. So we call equation +13 X plus eight Y equals to an equation to will be X minus three Y equals 12. Alright. So we're told to use the addition method and with the addition method, what we want to do is we want to choose one of the variables. So in this case either X or Y. And we want the coefficient of that variable in one equation to be the same magnitude but different sign than the coefficient in the other. Okay so in this case let's choose to deal with X. Okay so in equation one we have three X. In equation to we have X. Okay so what we want to do with the addition method since equation one has three X. Is we want equation to to have negative three X. Okay. That way when we add them we will cancel out that variable. Okay, so in order to get negative three X. In equation two we need to multiply by negative three. So let's take equation one. Okay and we're gonna add it addition method to equation two multiplied by -3. Okay so equation 13, X plus eight Y equals to an equation two multiplied by negative three. So we have X times negative three gives us negative three X negative three Y times negative three gives us positive nine Y. And on the right hand side 12 times negative three gives us negative 36 K. So be sure that you're multiplying every term of your equation. Not just the term of interest. Okay We have to keep that equation consistent. Alright And then adding our addition method. That's what we want to do and we'll see that we get three X plus negative three executives. Zero. Okay and that's exactly why we've designed it this way is to eliminate that variable of XK sometimes this is called the elimination method. Okay we've gotten rid of the variable X. Which means we'll only have wise and numbers that allows us to solve for y. Okay so eight Y plus nine Y. Is 17 Y. On the right hand side two plus negative 36 is negative divided by 17. We get y. Is equal to negative two. Okay so we found a Y value using our elimination method or Sorry? Our addition method. Now what we need to do is find a corresponding X value. Okay, why alone is not a solution? We need a corresponding X value. So either of these equations we need to solve both equations. This is the solution has to satisfy both equations. So you can choose either equation in this case we're gonna go ahead and choose equation to um but you can choose equation one if you wanted. So we're gonna substitute Y. -2. Into equation two We get X -3 times y -2 equals 12. This is gonna be X negative three times negative two. That's gonna be plus six Equals 12. And subtracting by six X is equal to six. Okay? Whoops. Pink. Okay. And so we get an X. Value of X is equal to six. So now we can write our solution as the set containing the point that we found. Six negative two. Okay so the solution to the system is the set containing the 20.6 negative two. That's gonna be answer B. Thanks everyone for watching. See you in the next video.

In Exercises 19–30, solve each system by the addition method. x + 2y = 2 - 4x + 3y = 25

Key Concepts

System of Linear Equations

Addition (Elimination) Method

Solving for Variables

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