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Solve Simultaneous Equations for x and y Using Elimination











































Solve the following system of equations using the elimination method.

Show all the steps used to arrive at your final solution.


2x + 4y = -30

-2x + y = 10

Comments for Solve Simultaneous Equations for x and y Using Elimination

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Jul 03, 2012
Solve Simultaneous Equations Using Elimination
by: Staff

To solve simultaneous equations with two variables, one of the variables must be eliminated using either substitution or elimination.


The steps of elimination method are:

1) Select the variable to eliminate (it can be either variable).

2) Make the absolute value of coefficient for the variable selected (for elimination) is the same in both equations.

3) Either add or subtract both equations to eliminate the selected variable.

4) Solve for the remaining variable.

5) Substitute the value of the known variable into either one of the original two equations, and then solve for the unknown variable.



Solve for x and y

2x + 4y = -30

-2x + y = 10


A1. Select the variable to eliminate (it can be either variable). I select “x”.

A2. Make the coefficient for the variable selected the same in both equations. In this case the coefficient for “x” is already the same in both equations.

The coefficient = 2.

A3. Either add or subtract both equations to eliminate the selected variable. Since the sign of the coefficient for the “x” in each equation is the opposite of the other, we will add the two equations to eliminate the “x”.

2x + 4y = -30

-2x + y = 10
-----------------
(2x - 2x) + (4y + y) = -30 + 10


0 + 5y = -20

5y = -20


A4. Solve for the remaining variable.

5y = -20

5y / 5 = -20 / 5

y * (5 / 5) = -20 / 5

y * (1) = -20 / 5

y = -20 / 6

y = -4


A5. Substitute the value of the known variable into either one of the original two equations, and then solve for the unknown variable.

1st equation: 2x + 4y = -30

We already know that y = -4.

Therefore: 2x + 4 * (-4) = -30

2x + 4 * (-4) = -30

2x - 16 = -30

2x - 16 + 16 = -30 + 16

2x + 0 = -14

2x = -14

2x / 2 = -14 / 2

x * (2 / 2) = -14 / 2

x * (1) = -14 / 2

x = -14 / 2

x = -7


>>> final answer: x = -7, y = -4

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

Check your work by substituting the values for x and y in the 2nd equation.

-2x + y = 10

-2 * (-7) + (-4) = 10


14 + (-4) = 10

10 = 10, OK → the solutions for x and y are valid.





Thanks for writing.

Staff
www.solving-math-problems.com


Sep 02, 2012
Substitution?
by: Anonymous

Dear Staff,

What about substitution? Can you use the example and explain to me?

Thanks & Regards

Sep 02, 2012
Solve Simultaneous Equations Using Substitution
by: Staff

Using Substitution:


    First equation: 2x + 4y = -30

    Second equation: -2x + y = 10

    2x + 4y = -30

    -2x + y = 10

Solve the second equation for “y” :

       -2x + y = 10

    Add 2x to each side of the equation

       -2x + y + 2x = 10 + 2x

       -2x + 2x + y = 10 + 2x

       0 + y = 10 + 2x

       y = 10 + 2x

       y = 2x + 10


Substitute 2x + 10 for “y” in the first equation:

       2x + 4y = -30

       2x + 4*(2x + 10) = -30

       2x + 4*2x + 4*10 = -30

       2x + 8x + 40 = -30

       10x + 40 = -30

    Subtract 40 from each side of the equation

       10x + 40 - 40 = -30 - 40

       10x + 0 = -30 - 50

       10x = -30 - 40

       10x = -70

    Divide each side of the equation by 10

       10x = -70

       10x / 10 = -70 / 10

       x * (10/ 10) = -70 / 10

       x * (1) = -70 / 10

       x = -70 / 10

       x = -7

Substitute -7 for “x” in the equation y = 2x + 10:

       y = 2x + 10

       y = 2*(-7) + 10

       y = -14 + 10

       y = -4

Final Answer

x = -7, y = -4





Thanks for writing.

Staff
www.solving-math-problems.com


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