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

Question

In Exercises 5–18, solve each system by the substitution method.y = (1/3)x + 2/3y = (5/7)x - 2

Two equations for a system of linear equations: y = (1/3)x + 2/3 and y = (5/7)x - 2.

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 here is y equals 2/7, X minus 13/7 and y is equal to minus 1/ x minus 19/5. Okay, so let's go ahead and write our equation and we're going to label them so that we can refer to them later. So we'll say equation one is going to be Y equals 2/7, X minus 13/7. Okay, an equation two, Y equals minus 1/5 x minus 19/5. We're asked to use the substitution method. So for the substitution method we want to isolate one variable in one of the equations and then substituted in the other. And we'll see here that in both of our equations we already have Why isolated. Okay, so we can choose either of those two substitute. Let's go ahead and substitute one into two. Okay, so we're gonna substitute equation one Into equation two. Okay, and this is where it's handy to have labeled those equations. It just makes it easier to keep track of your work. So we substitute Why equals 2/7, x minus 13/7 Into the second equation while on the left hand side we're gonna have to over seven x minus 13/7. Taking on the right hand side we have minus 1/5 x minus 19/5. Now we've done that substitution, we just have an equation of X and constant terms. So we can go ahead and solve for X. We have denominator seven on the left hand side denominator five on the right hand side. So let's go ahead and find a common denominator and in this case it's gonna be 35. Okay so let's um multiply the entire equation by 35. Okay if we multiply on the left hand side by 35 or sorry by five we're gonna have two times five X over 35 K minus 13 times 5/30. Oops. 35 37 35. On the right hand side we're gonna have minus seven K. We're multiplying by seven on this side to get that common denominator over X minus 19 times seven over 35. Hey? Alright so we have the common denominator all the way across. And so we can multiply both sides by 35 and eliminate that denominator. So on the left hand side we're gonna have 10 x minus 65 on the right hand side we're gonna have minus seven X minus 133. Okay so moving the seven X. To the left hand side and moving the minus 65 to the right hand side we're gonna have 17 X Equals -68. Okay and last step dividing by 17. We're gonna have X. Is equal to minus four is we found an X. Value X. Is equal to minus four. What we need to do now is find a corresponding y value. Okay so let's let's scroll. I just wanna make sure we're remembering our equations. So we have X. Is equal to minus four. Okay now we can substitute this into either equation one or equation to in order to find the corresponding y value. Um We're gonna choose equation to in this case. Okay substitute X equals minus four into equation two. Now equation two we have minus 1/5 of x. Which in this case is minus one minus four k minus 19/5. This is gonna give us 4/ -19/5 is equal to -15/5 Which is going to be -3. Okay so our y value here is going to be y equals -3. Okay so we have our x. value, our corresponding y value. We just need to write the solution and the solution. It's going to be a single point and that point is -4 -3. Alright so this is going to correspond let's go back to our answer choices. This is going to correspond to answer a Okay we have a solution set with a single . -3. Thanks everyone for watching. See you in the next video

In Exercises 5–18, solve each system by the substitution method.y = (1/3)x + 2/3y = (5/7)x - 2

Key Concepts

Substitution Method

Linear Equations

Graphical Interpretation

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