Video: Solving a System of Two Linear Equations Simultaneously

Solve the simultaneous equations ๐‘ฅ โˆ’ ๐‘ฆ = 4 and ๐‘ฅ + ๐‘ฆ = 14.


Video Transcript

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

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

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

We now know that two ๐‘ฅ equals 18, and we can solve for ๐‘ฅ. We divide both sides of the equation by two to get ๐‘ฅ by itself. Two ๐‘ฅ divided by two equals ๐‘ฅ; 18 divided by two equals nine, so we know that our ๐‘ฅ 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 ๐‘ฆ. Iโ€™m going to use the second equation. The reason for that is Iโ€™m adding ๐‘ฅ plus ๐‘ฆ.

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

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

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