Solving linear systems by substitution | Algebra Basics | Khan Academy

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We saw in the last video system of equations. In this video, I will show you one of the algebraic methods Where do you need Two line graph To see where they intersect. This will give you an accurate ink response. And in next videos you will see More ways to do that. Now look for these two equations. The first x plus 2y equals 9, And the second 3x plus 5y equals 20. And if you did the same process that we did in the previous video, you can If you draw each of the two lines a graph, These are the two lines. They can be drawn either in the form of a cross diagonal Or the shape of a slope. They are in a typical form now. You can draw both lines and know Where will they meet? This could be the solution. However, it is difficult to reach with just looking To find out exactly where they meet. So find a way to do that. The method I will use is the replacement method. I will use one of the equations to arrive For one of the variables, then do the replacement here So again here. My help will explain to you what I mean. Let me find x using the first equation. So the first equation says x plus 2y equals 9. I want to get the value of x so let me subtract 2y from From Tove the equation. Me x equals 9 minus 2y This is what the first equation says. It has somewhat rearranged. As the formula shows, So to achieve the two equations, x must Check the limitation here. So I can put this here instead of x> In the first equation, you would have found that x Equal to this. Well, if x has to be equal to that So let me put those instead of x So the second equation is 3 times x And you start from x you write that: 9 minus 2y. 3 times 9 minus 2y plus 5y equals 20 This is why it was called the replacement method. I replaced it for x only. And the benefit of that is that I have one equation With unknown and one and I can now find the value of y. Do this 3 times 9 equals 27. 3 times negative 2y equals negative 6y plus 5y equals 20. Add negative 6y to 5y So the formula 27 minus y equals 20 Discount 27 parties To have _ let me write that from us. Let us discount 27 on both sides. On the left side 27 and -27 they cancel each other And you keep negative y equal 20 minus 27 Equals negative 7. Then you can hit both sides In negative 1, you would get y equal 7 Now we have found the value of y for the intersection point The two lines. y equals 7. So write it here y equals 7 Now that you know the value of y, you can find the value of x. x equals 9 minus 2y Do it. x equals 9 minus 2 times y = 2 times 7 Or x equals 9 minus 14, or x equals stipe 5 If using the replacement method you can Access points x and y Which achieve the two equations Point x is negative 5, y is 7. They achieve the two equations. You can check that. The first equation: negative 5 plus 2 times 7 equals negative 5 plus 14 Already equal to 9. The second equation: 3 times negative 5 equals negative 15, plus 5 times y: Plus 5 times 7 So negative 15 plus 35 is really equal to 20. So this achieves both equations. And if you want a graph of the two equations They will cross negative point 5 comma 7 Now, use your skill To solve the following speech issue. I give you that sum Two numbers equal 70 And the difference between them Equals 11 What are the two numbers? Let them proceed to solve this verbal issue So let us know some of the variables. Suppose x is the largest and y is It is the smallest number. This is just an arbitrary assumption, One is greater than the other The difference between them is 11 Now, the first assumption is that the sum of the two numbers is equal to 70 Means that x plus y must equal 70 The second assumption is that the difference between them equals 11 It means that the largest number minus the smallest Should be 11 This means that x minus y should equal 11. That’s all you assumed. You have two unknown equations. You have a system of two equations You can solve it using the replacement method. Find the value of x in this equation. Whenever you add y For both sides of the equation, what will the result be? On the left side, x remains on its own Because these two will cancel each other. At the right end, you would get x equal to 11 Plus y or y plus 11. So x equals 11 plus y Using the second equation. And you can substitute x in the first equation. So instead of writing x plus y equals 70, it can Replace x with this That we came to in the first equation in purple Now we adhere to it as a constraint to x in the first equation So if you put this as an alternative, you get y plus 11_. In place x Plus y equals 70 This x. And that constraint we took from this second equation Or from the second assumption. I’ve put y plus 11 instead of x Because this was the limitation that She gave it to me the second equation. So get y. You got y plus 11, plus y equals 70. The same is 2y plus 11 equals 70. Then if you subtract 11 from both parties you get 2y What will it be worth? 59. Then subtract 10 from 70, you get 60 She is 59. So 2y is 59 That can be written: 59 on 2 Equals 29.5 y is 29.5 Now what is the value of x? Well, you have found that x equals y plus 11. So x equals 29.5 _ this is the value of y that we just mentioned _ Plus 11. Add 10, you get 39.5. Then add 1 you get 40.5. And here you are saved. If you want to find the intersection of these two lines They will cross at 40.5 points, 29.5 points. You can use this equation to get to x Then you put this as an alternative. Duplicate ????? Duplicate ????????????????????? ??? ???? The important thing is to use the two restrictions Now, check your credibility on what you found. What is the sum of these two numbers? 40.5 plus 29.5 is already 70. The difference between them is 11 Two accusations, 11 away from each other I hope that you have benefited from this lesson.

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