### Video Transcript

Solve the simultaneous equations ๐ฅ minus ๐ฆ equals four and ๐ฅ plus ๐ฆ equals 14.

We have these two equations, and theyโre in a pretty similar format. One of them is saying ๐ฅ minus ๐ฆ equals something, and the other one is saying ๐ฅ plus ๐ฆ equals something.

To solve this equation, weโre going to use a process called the elimination. Weโre actually going to add both of these equations together. For our first line, we say ๐ฅ plus ๐ฅ equals two ๐ฅ. Then we can say negative ๐ฆ plus ๐ฆ equals zero. Those cancel out. And last, weโll add four plus 14 equals 18.

We now know that two ๐ฅ equals 18, and we can solve for ๐ฅ. We divide both sides of the equation by two to get ๐ฅ by itself. Two ๐ฅ divided by two equals ๐ฅ; 18 divided by two equals nine, so we know that our ๐ฅ equals nine.

After that, we can take this information that we were given and plug it in to one of the equations to solve for ๐ฆ. Iโm going to use the second equation. The reason for that is Iโm adding ๐ฅ plus ๐ฆ.

In the first equation, we have a negative ๐ฆ, so we would still be able to solve for ๐ฆ in this case, but it would take a few more extra steps. So letโs use ๐ฅ plus ๐ฆ equals 14. We want to plug in nine for the ๐ฅ value, to say nine plus ๐ฆ equals 14, but remember weโre trying to find out what ๐ฆ is.

To isolate ๐ฆ, weโll subtract nine from both sides of the equation. By taking nine away from the left side of the equation, weโre left with only ๐ฆ. Subtracting nine from 14 gives us five. Our ๐ฆ-coordinate will be equal to five; ๐ฅ equals nine; ๐ฆ equals five.