Download presentation

Presentation is loading. Please wait.

1
SYSTEMS OF EQUATIONS

2
**Substitution Method Ex. 1: 2x + y = 15 y = 3x so 5x = 15 and x = 3**

You now have to go back to one of your original equations where you will substitute the known value of x in order to determine the value of y We have been using the Substitution Property in our proofs. Now we are going to use substitution to solve systems of equations. 2x + 3x = 15 so 5x = 15 and x = 3 y = 3(3) = 9 Write your answer as an ordered pair (3, 9)

3
**Ex. 2 3x – y = 13 y = x + 5 3x – ( x + 5 ) = 13 3x – x – 5 = 13**

Now substitute back into one of the original equations to find y. y = = 14

4
**You may have to rearrange one of the equations before you do the substitution.**

x + 4y = 20 2x + 3y = 10 Rearrange: x = 20 – 4y Now substitute and solve for y: 2 (20 – 4y)+3y=10 so 40 – 8y + 3y=10 -5y = so y = 6 Find x: x + 4(6) = 20 x+ 24 = 20 x = -4

5
**If you add these two equations together, the y term drops out!**

Solving systems of equations by adding or subtracting equations Example: x + 5y = -7 3x – 5y = 15 Now substitute into either equation to find y: 2 + 5y = -7 5y = -9 y = -9/5 If you add these two equations together, the y term drops out! 4x = 8 x = 2

6
Example: 4x – y = 16 3x – y = 11 x = 5 4(5) – y = 16 20 – y = 16 y = 4 (5, 4)

7
**After substitution we find y = 14 (6,14)**

You may have to multiply one of the equations before you add or subtract: -3x + 2y = 10 2x – y = -2 Multiply this equation by 2 4x – 2y = -4 Now add the equations together x = 6 After substitution we find y = 14 (6,14)

8
**You may have to multiply both of the equations by a number to get a variable to cancel out.**

2x + 5y = 36 3x – 2y = -3 Multiply by 3 6x + 15y = 108 Multiply by 2 6x - 4y = -6 19y = 114 y= 6

Similar presentations

OK

Some problems produce equations that have variables on both sides of the equal sign.

Some problems produce equations that have variables on both sides of the equal sign.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google