Storyboard Text
- Hello class, do you know how to find the exact solution to a system of equations algebraically? One method that you can use is the substitution method. This is what we will be learning about today. Ready, lets start!
- The Substitution Method
- The first thing you want to do is isolate one of the variables on their own. For this system of equations, isolating x in the first equation is easiest. The first step is to subtract 4y like in the example. Next, insert the first equation into the second, just like the example shows. After that, use the distributive property and solve for y.
- x + 4y = 3 -4y -4yx = -4y + 32(-4y + 3) - 3y = 17-8y + 6 - 3y = 17-8y - 3y + 6 = 17-11y + 6 = 17 -6 -6-11y/-11 = 11/-11y = -1
- x + 4y = 32x - 3y = 17
- Finally, you insert the value of y into one of your original equations, and solve for x. You can double check your answer by inserting your x and y values into each equation. Now that you know how to use the substitution method, lets try another problem.
- For this next system of equations, we know that the first step is to either isolate x or y in one of the two equations shown. If you look at the second equation, you will notice that x is already by itself. This means that we can move onto the next step and insert the first equation into the second. After solving for y, you insert your y value into either original equation. For this example, y was inserted into the first equation. Last, solve for x.
- y = -1x + 4(-1) = 3x -4 = 3 +4 +4 x = 7
- x + 4y = 32x - 3y = 17
- (5 + 2y) + y = 925 + 2y + y = 925 + 3y = 92-5 -5 3y/3 = 87/3y = 29x + (29) = 92x + 29 = 92 -29 -29x = 63
- x + y = 92x = 5 + 2y
- Now lets practice what you learned! For this first equation, your answer should be x = 1, and y = 5 or (1, 5). If you didn't get the right answer, that's okay, I'll walk you through it, or you can look at the steps taken to solve it! First isolate x or y in either equation. Once that is done, insert the equation with an isolated value into the other. Solve for x or y. Last, plug your x value or y value into one of the original equations. Did you get the right answer now? If you still don't understand, go back to one of the previous explanations. After reading this infographic, you should now be an expert at using the substitution method.
- x + y = 6-x + y = 4x + y = 6 -y -y x = 6 - y-1(6 - y) + y = 4-6 + y + y = 4-6 + 2y = 4+6 +62y/2 = 10/2y = 5
- x + (5) = 6x + 5 = 6 -5 -5x = 1
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