Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form...
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Transcript of Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form...
![Page 1: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/1.jpg)
Solving Systems Using Elimination
![Page 2: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/2.jpg)
Elimination
When neither equation is in the slope-intercept form (y =), you can solve the system using elimination.
You can add equations to eliminate a variable.
Look for like terms that are opposites of each other (will add to zero).
![Page 3: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/3.jpg)
Example 1
5x – 6y = -32 3x + 6y = 48 Make sure like terms are lined up with each
other. Look for like terms that are opposites (in
this case the –6y and +6y are opposites). Add all the like terms (5x + 3x = 8x) (-6y +
6y = 0) (-32 + 48 = 16)
![Page 4: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/4.jpg)
Example 1
Now you have “eliminated” the y term and have a one-variable equation to solve.
8x = 16 So, x = 2 You have the first half of your ordered pair.
Plug in 2 for x in one of the equations to find y.
5(2) – 6y = -32
![Page 5: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/5.jpg)
Example 1
10 – 6y = -32 Subtract 10 from both sides. -6y = -42 Divide both sides by –6 y = 7 Check by replacing x with 2 and y with 7 in
the second equation. 3(2) + 6(7) = 48 6 + 42 = 48 That’s true, so the solution is
(2,7)
![Page 6: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/6.jpg)
Example 2
x – y = 12 x + y = 22 The y’s are opposites, so add like terms (x + x = 2x, -y + y = 0, and 12 + 22 = 34) Now your equation is 2x = 34. Divide both
sides by 2. x = 17
![Page 7: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/7.jpg)
Example 2
Replace x with 17 in the first equation to find y. 17 – y = 12
Subtract 17 from both sides. -y = -5 Divide both sides by –1. y = 5 Replace x with 17 and y with 5 in the
second equation to check. 17 + 5 = 22 That is true, so the solution is (17, 5)
![Page 8: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/8.jpg)
Not Always So Easy
Sometimes there are not like terms that will add to zero (eliminate).
You can multiply or divide all the terms by any number (except zero) to make opposites.
![Page 9: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/9.jpg)
Example 3
3x + 4y = -10 5x – 2y = 18 There are no opposite like terms. However,
if I multiply the second equation by 2, the y’s will be opposites. (The first equation will stay the same.)
3x + 4y = -10 10x – 4y = 36
![Page 10: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/10.jpg)
Example 3
Now add the like terms. 13x = 26 Solve. x = 2 Replace x in the first equation with 2 to find
y. 3(2) + 4y = -10 6 + 4y = -10 Subtract 6 from both sides.
![Page 11: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/11.jpg)
Example 3
4y = -16 Divide both sides by 4 y = -4 Check by replacing x with 2 and y with –4
in the second equation. 5(2) – 2(-4) = 18 10 + 8 = 18. This is true. The solution is (2, -4)
![Page 12: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/12.jpg)
Example 4
7x – 12y = -22 5x – 8y = -14 I choose to get rid of the x’s. So I will
multiply the top equation by 5 and the bottom equation by -7
35x – 60y = -110 -35x + 56y = 98 Now add the equations.
![Page 13: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/13.jpg)
Example 4
-4y = -12 Y = 3 That is the second member of the ordered pair.
Now find x by replacing y in one of the equations with 3 and solve for x.
7x – 12(3) = -22 7x – 36 = -22 7x = 14 X = 2 (2, 3)
![Page 14: Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.](https://reader035.fdocuments.net/reader035/viewer/2022071807/56649dce5503460f94ac238e/html5/thumbnails/14.jpg)
Try these…
2x + 7y = 31
5x – 7y = -45 x – 6y = 2
6x + 6y = 12 2x + 5y = 34
x + 2y = 14 x + 6y = 20
x + 2y = 12
(-2, 5)
(2, 0)
(2, 6)
(8, 2)