Notes here, and on pages 365-368 in book

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Steps for Addition:

1) **Align** x's over x's and y's over y's. Will likely require some movement via the commutative property or adding of opposites to get variables in the correct spots.

1b) **Create opposite terms**: You may need to multiply one or both equations by -1 or some other number in order for the x's or the y's to be opposites.

2) **Add** If 1 (and 1b) are done properly, one of the variables will be eliminated (why this is sometimes called the elimination method).

3) **Solve** the new equation which now has only one variable

4) Use the value of the variable to **plug in** to one of the original equations to find the missing side of the coordinate pair.

Example:

For the equations, x-y=2 and y+3x=10

What are the coordinates of the simultaneous solution?

ALIGN: In this case just move around the first equation to make it -y+x=2

Add:

y+3x=10

-y+x=2

Gives: 4x=12

SOLVE: 4x=12 this means x=3

PLUG IN: Pick either of the two equations to plug in x=3. You should get the same answer for y.

-y+3=2

gives

y = 1

whereas

y+3(3)=10

also gives

y=1

So the solution is (4,1)

Harder Example:

For the equations, x+y=1 and 3y-7=-4x

What are the coordinates of the simultaneous solution?

ALIGN: In this case just move around the second equation to make it 4x+3y=7

Adding:

4x+3y=7

x+y=1

DOES NOT ELIMINATE X or Y

MUST DO STEP 1B and Multiply second equation by -4 (or -3) to create opposite terms

Adding:

4x+3y=7

-4x-4y=-4

Gives: -y=3

SOLVE: -y=3 this means y=-3

PLUG IN: Pick either of the two equations to plug in y=-3.

x+-3=1

x=4

So the solution is (4,-3)