System of addition problem?

1) 4x + 7y = 7

2) 2x - 3y = -2

First modify one or both equations so the coefficients of one of the variables are equal with same or opposite sign

3) -4x + 6y = 4 {multiply equation 2 by -2}

7y + 6y = 11 {add equations 1 & 3}

13y = 11

y = 11/13

1) 4x + 7(11/13) = 7

4x + 77/13 = 7

4x = 7 - 77/13 = 91/13 - 77/13

4x = 14/13

x = (14/13)/4 = (7/13)/2

x = 7/26

2) 2(7/26) - 3(11/13) = - 2 {check answer}

14/26 - 33/13 = - 2

14/26 - 66/26 = - 2

- 52/26 = - 2\\- 2 = - 2

In the heat of a test you might not have time to check the answer, but while you are learning it is a good idea to verify your work

When you solve by addition method (sometimes called combination method) you want to make sure that your co-efficients "match" for one of the variables, except that it should have the opposite sign. That means that if you have a 4x in one equation, you need a -4x in the other equation.

So, take this one.

4x+7y=7

2x-3y= -2

The easiest way to do it is to multiply the whole second equation by negative 2.

2x-3y= -2

-4x + 6y = 4

All I did was double each term and switch the sign.

Now, let's take the original equation, and then right below it let's write the new version of the second equation.

4x+7y=7

-4x + 6y = 4

Then add straight down. The 4x + (-4x), the 7y+6y, and the 7+4.

4x+7y=7

-4x + 6y = 4

___________

0 + 13y = 11

So now you have a normal linear equation, 13y = 11.

Divide both sides by 13

13y= 11

y = 11/13

Then you can substitute that value of y into either of the original equations.

4x+7y=7

4x + 7(11/13) = 7

4x+77/13=7

It's sort of ugly from there but it's just arithmetic.

I hope that helps.

If you need more practice with algebra, this is an awesome resource: http://www.math.com/students/worksheet/algebra_sp....

4x + 7y = 7.

2x - 3y = - 2. Solve by addition.

Multiply the second equation by - 2.

4x + 7y = 7

- 4x + 6y = 4. Add the two equations together. The x terms cancel to zero.

13y = 11. Divide both sides by 13.

y = 11/13. Answer for y. Substitute this value for y in either original equation and solve for x.

4x + 7y = 7.

4x + 7(11/13) = 7. Multiply all terms by 13 to cancel out the 13 in the denominator.

13(4x) + 7(11) = 13(7).

52x + 77 = 91. Subtract 77 from both sides of the equation.

52x = 14. Divide both sides by 52.

x = 14/52. Reduce by dividing numerator and denominator by 2.

x = 7/26. Answer for x.

Answers: x = 7/26, y = 11/13.

Check Answers: Put the values of x and y in the second equation and see if it checks.

2x - 3y = - 2.

2(7/26) - 3(11/13) = - 2.

7/13 - 33/13 = - 2.

- 26/13 = - 2.

- 2 = - 2. Checks OK

4x+7y=-7

2x-3y=-2

4x+7y=7

-2(2x-3y=-2)

4x+7y=7

-4x+6y=4

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

13y=11

y=11/13

2x-3(11/13)=-2

2x-33/13=-2

2x-33/13+33/13=-26/13+33/13

2x=7/13

x=7/13*1/2=

x=7/26

what do you mean by that ??

cramer's rule is faster if you'd like the solution almost instantaneously.