This week I learned how to solve systems of linear equations.

For example, this is the equation: x + y = 9, x – y = 1

First, you have to rearrange the equation to isolate y.

Then the equation looks like y = 9 – x,   x – y = 1. After that we have to combine the two equations to get y. We insert “9 – x” into y. It becomes x – ( 9-x ) = 1. Then we combine like terms by bringing 9 to the other side of the equal sign. It will become “x + x = 9 + 1”.  Then we do ” x + x = 2x” and “9 + 1 = 10”. Then we simply the equation: 2x/2 = 10/2. The final answer is “x=5”.

But, we still have to solve for y. So we take “x=5″ and insert it into the original equation where x goes. ( x – y = 1) .

It will look like this: 5 – y = 1. Then we isolate y, so we bring y to the other side and 1 to the side that “y” was on. That would look like this: 5 – 1 = y. Then we subtract 1 to 5. The final answer to the equation is “x=5” and “y=4”.

Another equation is: 4x + y = 0,   7x + 4y = 3.

First we take “4x + y = 0” and isolate y. It will look like this: y = -4x.

Then we insert “y = -4x” into “7x + 4y = 3“. It will look like: 7x + 4 (-4x) = 3. Then we start with the brackets and distribute 4 into -4x. Then the equation will look like this: 7x – 16x = 3. 

After that, we have to combine like term. So, we do “7x – 16x“. That will be “-9x”. Then we solve “-9x/-9 = 3/-9”. The final answer will be: x= -1/3.

Now we have to solve for y. So, we insert “x= -1/3” into the original equation. (4x + y = 0)

It will be 4(-1/3) + y = 0. Then we distribute 4 into -1/3. That will be “-4/3 + y = 0“. For the final step, we have to isolate y. The final equation is: “x = -1/3” and “y = 4/3”.