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Addition/Subtration Methods for Algebra

by Christine
(Virginia)











































Solve the following equation by using the addition/subtraction method. The numbers are x = 2 and y = 7
Step 1: Write both equations in the form ax + by = c
Step 2: Multiply the second equation by 2 in order to make the coefficients of the x terms
Step 3: Subtract the second equation from the first equation to eliminate the x variable.
Step 4: Solve the equation for y.
Step 5: Select one equation and substitute 4 for y and solve for x.

Comments for Addition/Subtration Methods for Algebra

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Oct 15, 2012
addition/subtraction method
by: Staff


Answer:


Hi Christine,

You left the equation out of your problem statement.

Just attach it as a comment.



Thanks for writing.

Staff
www.solving-math-problems.com


Oct 15, 2012
Follow up
by: Christine

Okay this is what I have so far. I am trying different numbers as I go to see what is the easiest way to understand this. I believe some of my steps are correct but I am concerned about the others. Any insight about this would be greatly appreciated.

3. Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps. Use the example on page 426 of Mathematics in Our World as a guide.

Step 1: Write both equations in the form ax + by = c
x + y = 6
3x + 2y = 13

Step 2: Multiply the second equation by 2 in order to make the coefficients of the x terms
(-2)*(x + y) = (-2)*6

-2x + -2y = -12

-2x + -2y + 2y = -12 + 2y
-2 x + 0 = -12 + 2y

-2x = -12 + 2y

Divide each side by '-2'.
x = 6 + -1y


Step 3: Subtract the second equation from the first equation to eliminate the x variable.

-2x - 2y = -12
3x + 2y = 13
-------------------
-2x - 2y + 3x + 2y = -12 + 13
-2x + 3x - 2y + 2y = -12 + 13

x + 0 = 0

x = 0

Step 4: Select one equation for y and solve.

x + y = 6

0 + y = 5

y = 5

Step 5: Select one equation and substitute 4 for y and solve for x.

Oct 15, 2012
addition/subtraction method
by: Staff


Answer 2:

Hi Christine,


Step 1: Write both equations in the form ax + by = c

x + y = 6

3x + 2y = 13

If these are your two equations, they are written correctly.


Step 2: Multiply the “first” equation by (-2) in order to make the coefficients of the “y” terms the same in both equations (so they will cancel when added)

(-2)*(x + y) = (-2)*6

-2x + -2y = -12

You are correct up to this point.


Step 3: “Add” both equations to eliminate the y variable. (Add, rather than subtract. There is already a -2y in the first equation. -2y + 2y = 0, which is what you want.)


-2x - 2y = -12
3x + 2y = 13
-------------------
(-2x + 3x) + (- 2y + 2y) = -12 + 13

(-2x + 3x) = x

(- 2y + 2y) = 0

-12 + 13 = 1

(-2x + 3x) + (- 2y + 2y) = -12 + 13

x + 0 = 1

x = 1



Step 4: Select one equation for y and solve.


x + y = 6

1 + y = 6

1 + y - 1 = 6 - 1

1 - 1 + y = 6 - 1

0 + y = 5

y = 5


Final Answer:

                 x = 1, y = 5


Graphically, the solution is the intersection of the plot of both equations:

 Math – Solution of Two Linear Equations







---------------------------------

Check the answer by substituting 1 for x and 5 for y in both of the original equations.

x + y = 6

1 + 5 = 6

6 = 6, OK


3x + 2y = 13

3*1 + 2*5 = 13

3 + 10 = 13

13 = 13, OK


Since x =1 and y = 5 satisfy both of the original equations, these values are correct.


Thanks for writing.

Staff
www.solving-math-problems.com

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