Download presentation

Presentation is loading. Please wait.

Published byIra Milton Cox Modified over 5 years ago

1
Dr. Fowler CCM Solving Systems of Equations By Substitution – Harder

2
Solving a system of equations by substitution Step 1: Solve an equation for one variable. Step 2: Substitute Step 3: Solve the equation. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Pick the easier equation. The goal is to get y= ; x= ; a= ; etc. Put the equation solved in Step 1 into the other equation. Get the variable by itself. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations. ALREADY IN NOTES – Read Only for Review

3
1) Solve the system using substitution 3y + x = 7 4x – 2y = 0 Step 1: Solve an equation for one variable. Step 2: Substitute It is easiest to solve the first equation for x. 3y + x = 7 -3y x = -3y + 7 4x – 2y = 0 4(-3y + 7) – 2y = 0

4
3y + x = 7 4x – 2y = 0 Step 4: Plug back in to find the other variable. 4x – 2y = 0 4x – 2(2) = 0 4x – 4 = 0 4x = 4 x = 1 Step 3: Solve the equation. -12y + 28 – 2y = 0 -14y + 28 = 0 -14y = -28 y = 2 1) Solve the system using substitution

5
3y + x = 7 4x – 2y = 0 Step 5: Check your solution. (1, 2) 3(2) + (1) = 7 4(1) – 2(2) = 0 1) Solve the system using substitution Answer is (1,2)

6
2) Solve the following system using the substitution method. 3x – y = 6 and – 4x + 2y = –8 STEP 1 – Solve the first equation for y is easiest, 3x – y = 6 –y = –3x + 6 (subtract 3x from both sides) y = 3x – 6 (multiply both sides by – 1) STEP 2 – Substitute this value for y in the OTHER equation. –4x + 2y = –8 –4x + 2(3x – 6) = –8 (replace y to other equation) –4x + 6x – 12 = –8 (use the distributive property) 2x – 12 = –8 (simplify the left side) 2x = 4 (add 12 to both sides) x = 2 (divide both sides by 2) CONTINUED >

7
STEP 3 – To get y, substitute x = 2 into either original equation. The easiest is the one that was already solved for y. y = 3x – 6 = 3(2) – 6 = 6 – 6 = 0 y = 0 We have now found x & y. Answer is (2, 0)

8
EXAMPLE 3 TRUE – The answer is infinitely many solutions Solve the system by the substitution method. Solve first for x:Substitute:

9
EXAMPLE 4 Use substitution to solve the system. Solve first for x: Substitute into other equation: To get X, substitute y you found into equation already solved for X:

10
Example #5: x + y = 10 5x – y = 2 Step 1: Solve one equation for one variable. x + y = 10 y = -x +10 Step 2: Substitute into the other equation. 5x - y = 2 5x -(-x +10) = 2

11
x + y = 10 5x – y = 2 5x -(-x + 10) = 2 5x + x -10 = 2 6x -10 = 2 6x = 12 x = 2 Step 3: Simplify and solve the equation.

12
x + y = 10 5x – y = 2 Step 4: Substitute back into either original equation to find the value of the other variable. x + y = 10 2 + y = 10 y = 8 Solution to the system is (2,8).

13
Excellent Job !!! Well Done

14
Stop Notes Do Worksheet

Similar presentations

© 2021 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